The Witch has a few good options. Her Slumber Hex can put a creature of any HD to sleep, and is based off of her hex save. Which scales with her. (DC 10+ 1/2HD + INT) She also gets a grand hex, called Eternal Slumber, which is a permanent sleep effect. Now this has the bonuses of not needing to fascinate a creature first, (Relying only on one save instead of two, and being a bit more combat viable) but has the drawback of only being able to target the same creature once.

The Dreamspun sorcerer is also worth a one level dip as well (If selecting another class. They can perform just as well as other classes and get some extra options vs sleeping opponents!), as they get an innate ability that functions like lullaby, but with a -4.

Being a sorcerer or witch will also allow you access to higher level spells. This can be useful for metamagics to heighten the spell, casting it up to 9th level to increase DC. Or add the Traumatic Spell Metamagic (Keep in mind this may need to be used with other spells, IE something that causes shaken or fear)... Making them take nightmare damage as you put them to sleep!

The too long, didn’t read here is simple: defense is not something the barbarian is ever going to do well. Trying will only hurt your offense, without appreciably improving your defense. Your survivability comes from killing things dead. Basic armor (maybe mistmail), a cloak of resistance, and invulnerable rager abilities are quite sufficient here, or at least the best you’re going to reasonably get. When you can, nightmare boots, a cloak of displacement, and things that grant you death ward, freedom of movement, and/or mind blank are worthwhile, but ultimately, don’t sweat it. Your spellcaster allies are really the ones responsible for neutralizing threats before you can kill them. Your job is to kill them.

To understand why this is the answer, and any attempt to bolster your defenses is only going to hurt you, there are a few facts of Pathfinder that you need to understand first:

Pathfinder is not a balanced game

Not every class is equally capable. Not every class is equally flexible. Some classes are very limited in what they can and cannot do. Some classes cannot do much of anything outside their specialty. Some of those classes aren’t even that good at that specialty. This is an unfortunate reality, but it is reality and you have to understand it.

People who analyze Pathfinder and its imbalances organize classes into tiers, from 1, classes that can do everything, to 5, classes that can only do one thing and even that not particularly well, or struggle doing a mish-mash of things. See What tier are the Pathfinder classes? for more details.

Barbarian is not a flexible class

Barbarians deal damage. That is what they do. They aren’t necessarily the best in the game at it, but they’re pretty good at it.

They are not good at anything else. They cannot be made to be. Attempting to do so will only throw away lots of damage potential for extremely limited skills in other fields.

That puts barbarian in tier 4. They’re pretty good at damage-dealing, and that’s a pretty important thing to be good at, so they’re better than several classes, but it still puts barbarians on the lower end here.

The best defense is a strong offense, anyway

Other classes can try to get some defenses. High-Dex can give you decent AC, magic can give you other non-AC defenses, and so on. Barbarians don’t have those options, particularly high-Strength barbarians like you (a barbarian might be able to try doing a high-Dex finesse barbarian approach, maybe, but that isn’t your character).

But ultimately, that only matters so much. Pathfinder is a very glass-cannon-y game. At low-mid levels (above 1st or 2nd or so, but below 10th to say the least), there can be some back and forth, but at high levels (and the very earliest levels), it really is rocket tag (warning: TVTropes link). Consider this analysis of what it takes to maintain relevant AC. A high-Dex character needs to spend nearly 20% of his or her wealth to maintain AC at 20th level (and to maintain it at all levels can take as much as 95%!). For a heavy-armor, low-Dex character, that number is 35% at 17th, and it isn’t even possible beyond that point.

And that’s only AC: AC is the worst defense in the game. Too many things ignore it, and most of the time it only protects you from hp damage (which only matters once you run out, while a failed saving throw often means you lose immediately). So optimal characters will fall behind in AC regardless, because it costs too much to do otherwise.

So you’re right, this is a bad houserule. There is nothing about the barbarian class that justifies nerfing it. But ultimately, it doesn’t really matter. All it really means is that you’ll start falling behind, and ignoring, your AC slightly earlier than you might otherwise—maybe. Personally, I prefer light armor most of the time, because the cost, weight, and armor check penalty of medium or heavy armor isn’t worth it to me. I would also very likely sell that ring of protection, because it’s worth a whole lot in gold pieces, while its deflection bonus to AC isn’t worth a whole lot to me (though, deflection is much better than armor or natural armor or shield).

So your best hope for survivability is to play to your strengths, and kill things dead before they get a chance to pose a threat. Throwing away lots and lots of damage potential only leaves threats more opportunities to hurt you, and you cannot trade that damage potential away for similarly-strong defenses. Those defenses simply do not exist for you to take. At very-low levels, you need to pick up the basics, and at very-high levels there are some potent options, but in between, really, just focus on killing things.

On having a strong offense

Use a two-handed weapon. Have, and use, Power Attack and Furious Focus. A furious weapon isn’t a terrible choice. Choose the Beast Totem, and get pounce at 10th level. Consider getting a mount, a lance, and Spirited Charge. Or even worship Gorum, or your setting’s equivalent, and taking his Greatsword Battler divine fighting technique—then you can take the Vital Strike line and put it to solid use (probably better than any other class).

But the goal here is simple: you charge things, and kill them. Dead and destroyed things can’t hurt you.

If you want a little more flexibility, barbarians are also pretty good at the Intimidate game; still offense, but gives you a little more ability to deal with things you can’t kill outright. Cornugon Smash is pretty solid. Intimidating Prowess, however, is an obnoxious feat tax, but you’d probably need it to go this route.

Leave protecting people to the spellcasters

That’s what they’re there for. They should be dividing foes with walls, blinding foes with darkness or clouds or just straight blinding them, hampering foes’ actions, and so on and so forth. In the face of competent spellcasting, your enemies should not be able to mount a significant offense in the first place. Battlefield control, debuffing enemies, and buffing allies are some of the best uses of magic.

Dealing damage, that is, blasting, is a really poor use of magic. They should let you deal the damage, you’re made for it and there are so many more important things they need to be doing.

Personal defenses you should have

There are certain, basic, entry-level defenses that every character should always have, even if the spellcasters are protecting people with debuffs and battlefield control. They’re just really cheap and easy to get, so there’s no reason not to.

1. Mundane armor that is the best in its weight class and that you have proficiency with from your class—for you, a chain shirt or leather lamellar. Mundane armor is cheap and even if armored AC is low-value, it tends to give you a big wodge of it for effectively nothing.

   • If not using a weapon: a buckler, light shield, or heavy shield. Darkwood or mithral if necessary to avoid armor check penalty, arcane spell failure, and/or nonproficiency penalties (if ACP is 0, nonproficiency with a shield has no drawback). Since you are a barbarian, you are weapon-based, and should not use a shield anyway. But for people who don’t care about weapons, this is an almost-free boost to AC, and another platform for magical properties.

2. A +1 enhancement bonus to your armor. Mandatory for any other magic.

   • A +1 enhancement bonus to your shield, if any. Mandatory for any other magic, which is really the whole reason to bother with a shield in the first place.

3. The highest-bonus cloak of resistance you can afford. Cloaks of resistance apply to all saves, so unlike armor they apply to a huge array of particularly-dangerous effects, and they are reasonably priced. Always get the best you can.

Beyond that, other options are mostly terrible, but there are a few things worth mentioning, especially if you can get them for mere gold instead of having to spend feats and class features on them.

• Using a shield alongside a weapon. Cuts way too hard into your offense; not worth it.

• Higher enhancement bonuses to armor or shields. Don’t buy these; they are overpriced. Special armor properties (discussed in more detail below) are the real benefit of magic armor.

• Better armor due to Armor Proficiency feats. No! Feats are precious, precious things. A +2 bump to armored AC, particularly when tacked on to larger armor check penalties and slower speeds, isn’t worth very much at all.

• An amulet of natural armor of any kind. These cost the same as enhancement bonuses to armor, and cannot have special armor properties. Pass for the same reasons you pass on higher enhancement bonuses to armor.

• A ring of protection of any kind. More debatable, but ultimately these are really expensive for a relatively-small boost. Deflection bonuses are good, but the amount of gold they’re worth is better-spent elsewhere. Maybe a ring of protection +1 is OK enough; since the cost scales quadratically the +1 version isn’t too bad, and ya know, you already have one.

• Toughness. Toughness is a mediocre feat for a low-hp class like wizard. For a high-hp class like barbarian, it’s a complete waste of time. Your big HD, high Constitution, and bonuses from rage should cover your hp well. There are more important things to use feats on.

• Healing of your own. You’re a barbarian, you can’t heal people, not even yourself. Renewed Vigor and Regenerative Vigor are terrible rage powers; spending a standard action in combat is an enormous cost (you are probably only going to get 2-3 of those in a given fight), and it’s a tiny amount of healing. Let the spellcasters heal you (and help them buy wands of cure light wounds).

• Damage Reduction from invulnerable rager. This is pretty solid; the number isn’t terribly large but it’s much bigger than you usually see, and the cost isn’t very high (uncanny dodge is pretty good, but improved uncanny dodge is pretty niche and the regular barbarian DR is minuscule, and trap sense is garbage). You are already ahead of the game by having this.

• Damage Reduction from items, feats, or other class features. Damage reduction almost-always has one of the following flaws:

  • it comes in very small amounts (like the regular barbarian DR),
  • it is exceedingly conditional or limited (like Bolstering Resilience’s bonus against a single attack, that then leaves you fatigued, or Stalwart needing you to nuke your offense using Total Defense or Combat Expertise), or
  • is bypassed by magic (which means it’s ignored by every real threat anyway).

  It also costs massively to get those small amounts—feats, rage powers, these are precious, precious things. They aren’t worth the cost. (This is especially true for an invulnerable rager, since most things won’t stack with the DR you already have. But really, even if you weren’t an invulnverable rager, you still shouldn’t get these.)

• Miss chances. These are very good defenses, because they work equally-well against all opponents. Against particularly-dangerous opponents, that’s an advantage because it ignores their skills (and against not-particularly-dangerous opponents, we don’t care). A mistmail is a fine armor, for example: 3 minutes’ worth of 20% miss chance is a great deal at 2,250 gp. Paying for improved versions that have more uses per day, or simply buying more mistmails and changing between combats, is a really good choice as you level—or would be, if it weren’t for the excellent nightmare boots that you could buy instead. At higher levels, a cloak of displacement is fantastic. You can also ask your GM about possibly commissioning custom items of blur and/or mirror image for more miss chances; these arguably stack since they are for different reasons.

• Immunities. The endgame, these are the real goal—effects you don’t have to worry about at all are effects that you’ll be happy to have enemies waste time trying. Death ward, freedom of movement, and mind blank are the best examples, and the latter two come in (very expensive) ring form. Death ward could be accessible from a (also likely expensive) custom magic item; speak with your GM once you get high enough in level to be considering these expenses. Fortification armor properties also fall in this category.

• Special armor properties. In addition to the aforementioned fortification, armor properties are a relatively-cheap way to get defenses. Since AC ends up being too difficult to bother with, most armor properties are worth more than their equivalent enhancement cost to you. They can also offer other, more unusual features, like delving’s 10-ft. burrow speed, a rather interesting option that could allow you to bypass ambushes and get the drop on opponents by coming from unexpected angles. I recommend avoiding spell resistance, though; the numbers aren’t great and you’re just as likely to resist your ally’s buff or healing spell as you are to avoid the enemy’s attacks. Note that some of these, like stanching, may make enhancement bonuses to your armor more valuable than they’d otherwise be, but that also plays against them because they effectively cost more than they appear as you need to get otherwise-useless enhancement bonuses.

  • +1 animated darkwood heavy shield with other properties. At the very high-end, it may be cheaper to add new special properties to a +1 animated darkwood heavy shield than to add the same property to your armor. A darkwood heavy shield has no armor check penalty (so you take no penalties for using it without proficiency), and since it’s animated it doesn’t interfere with your offense. Also offers a +3 shield bonus to AC, but you really shouldn’t care by the time this becomes a sensible option. You may very likely never reach the point where you actually want one of these.