I'm 'afraid' you're right about your assessment, and I don't know of any other rules either.
However, I'm not sure why you think two weapon fighting is unbalanced, as enemies and PCs use the same rules for it, afaik. They can also suffer the same setbacks, such as being practically unable to grab the rope swinging by when the ship they're fighting on takes a wild tumble etc. (Sure, such cases aren't really covered by the rules, but that shouldn't stop you from coming up with critical events and matching improvised situational modifiers and tests to enliven your battles.)
Using two weapons (which, let us keep in mind, also include shields in WFRP) is a bit more efficient than using one, just as using one is a bit more efficient than using none -- and imo that sounds reasonable in real life as well, especially when you view combat through the lens of heavy abstraction most rpg systems, WFRP2 definitely included, utilize. And it's an option anyone can take advantage of. Arm your NPCs appropriately. ;)
Ultimately, this is all your call as DM and how/if you want to accommodate your campaign development to make any changes.
From a rules perspective, players get a free action (PHB pp190) that allows them to do things like draw/sheathe weapon, pick up a dropped item, etc.
Shields further require an action to don/doff (PHB pp146). Given that they add +2 to AC, that is a big boost and possibly why they require the action in order to gain such a bonus.
The use of two-handed weapons can also be seen as a balance issue. You are choosing bigger attacks over more defense. If you opt to let someone with a two handed weapon also get the benefit of the shield, you are greatly increasing the capabilities of that character.
There is a downside to allowing them to switch between their 2-handed weapon and shield at will: any out-of-turn actions (like Opportunity Attack reactions) will be without their primary weapon. They'll be using unarmed strikes or improvised weapon which would deal either only 1d4 if using the shield to attack (no proficiency bonus), or 1 damage if using unarmed strike.
Letting them don/doff the shield without penalty during combat basically gives them an extra 2 actions if you go purely by the rules AND they still get to get the damage benefits of the two-handed weapon. If they also have the Great Weapon fighting style and/or feat, then the balance becomes even worse.
Many of the combat/feat/fighting styles lean towards either being a DPR tank or a damage soaking tank. Letting someone get both could unbalance, but you as the DM are generating the combat scenarios and can accommodate for anything you give (or don't give) your players.
I also wouldn't get too hung about that character "being the only tank." Having a tank isn't required, just like having a healer isn't required.
Potential Solutions
Provide a means of access to magic protection (better armor, magical armor, ring/cloak of protection).
Give them access to Shield of Faith (via feat Magic Initiate), but still maintain the concentration mechanic. This will give them the +2 they're looking for, but at a risk.
Best Answer
Armor Class has historically represented your ability to avoid taking the brunt of a hit, not your ability to avoid the hit.
When your characters are in melee, don't assume they're all standing still staring at each other. They're constantly in a state of brawl, swinging blades, trading jabs, parrying, shifting around, etc. This is why there are penalties for Ranged Attacks vs. characters in melee.
What attack actions represent are the notable combat actions that constitute dealing meaningful blow to your opponents. Like two samurai fighting when one breaks away and manages to get a heavy strike in. I'll be using a Samurai Duel as an example throughout this answer.
Let's look at the formula for Armor Class in a past edition. D&D 5e has changed a lot of things, but it still had its beginnings here.
Dexterity and Dodge Bonuses
These bonuses contribute how likely you are to dodge an attack outright. In this situation, a Samurai will go in for a strike and the other Samurai will sidestep it.
Size Bonus
The size bonus/penalty represents the how your size contributes to a sort-of passive dodge. You're harder to hit when you're small because just your general movements would make you harder to hit. A goblin samurai is shifting back and forth against a human samurai. Since the goblin is small, the human samurai needs to hit a smaller target which is generally harder to do. The goblin isn't trying to dodge, it's just moving around.
Deflection Bonuses
Deflection bonuses represent parts of armor or your body that will take a hit and divert most of its force away from you. The shape of the armor-clad samurai's helmet diverts a head strike from an annoyed Ronin.
Armor and Shield Bonuses
Your Armor and Shield Bonuses contribute to how likely an enemy is to hit your armor or shield instead of your actual body.
Natural Armor Bonuses
For when your armor doesn't help, but your rock-hard skin does. Natural armor is the part of your body you don't mind getting hit in. If you've got wood for skin and someone's swinging a katana at you, it could very well get caught in that thick, woody membrane. The Shogun learned this lesson the hard way when when a treefolk swordsman challenged him to duel.
In D&D 5e, a lot of this is unspoken or hidden away
Now, your "Armor Bonus" is masked by being your new "Base Armor". Most modifications to your Armor Class will follow similar logic in terms of what's actually happening when you get attacked. For example, in D&D 5e, Mage Armor changes your Base AC to 13. What this really amounts to is instead of being naked with a Base AC of 10, you've got a +3 chance for an attack to hit your Magic Armor, instead of hitting you. It's still generally the same concept.
Now, back to your goblin example
You said you have 19 AC. Let's say for the sake of a meaningful example, your AC breaks down in the following way:
That base 11 is really 10 from general brawling movement and +1 from actually wearing armor at all. We don't really care what that last +4 is from. Let's say something magic.
Next, let's assume that the Goblin doesn't have any bonus to it's Attack rolls. It rolls a 1d20 and uses that roll only to see if it hits you.
Closing Notes
When Armor Class and Attack Rolls get REALLY high, you don't always get to break it down like this. Eventually, enemies won't miss you because you were moving. They still hit you when you're dodging. When an enemy is well out of your league, sometimes the only reason you didn't get hit is the skin of your teeth giving you that 1/20 chance to avoid a fatal blow. But at the very least, your enemy wasn't just swinging at the air when they rolled lower than your AC.