Based on the stats given, it appears to me that your best option is to not multiclass.
The most obvious option would be a dip into Monk, to get Unarmored Defense's Wis-to-AC bonus, but that would be trading leather's +1 for your Wisdom's +1. The other abilities wouldn't really add anything to what you already have.
Another option is Barbarian's Unarmored Defense. That would add +2 AC from your Con instead of your Leather armor, but simply changing to Studded Leather (also light, and giving full dex bonus) would achieve the same result. The Barbarian's Rage does add a moderately useful ability, but comes at the expense of delaying your progressing in Fighter/Monster Hunter.
Finally, a 2 level dip into ranger would allow you to pick a second fighting style, specifically "Defense" which grants +1 AC while wearing armor. Again, the Ranger's abilities do not synergize particularly with your other abilities, and delaying your main class abilities for 2 more levels is unlikely to be worth +1 AC.
Also note that none of these options combine. Unarmored Defense is specifically called out under multiclassing as an ability you can only get from a single class, and even the greatest Cheeselords still have trouble finding a way to be unarmored and wear armor at the same time.
It seems like you already have the best option figured out: take the Dual Wielder feat for the bonus AC, and indirect damage increase of 2 one-handed weapons.
While you're shopping for a second rapier, upgrade to a suit of studded leather. This and Dual Wielder will bring you up to 17 AC.
After that, just stick with fighter. At 7th level you can start using 2 superiority dice on damage, as well as automatically maxing superiority dice damage against certain types of enemies. At 10th level, your superiority dice get bigger by a step, becoming d10's.
These options will do more for you than you can get from any quick dips into other classes.
For a build like yours, and for most builds in 5e, multiclassing is a great way to increase the breadth of your skills and abilities, but usually does not add a lot to the depth of them.
As Ethan has pointed out in the comments, don't forget to turn to your teammates for assistance and buffs, as well as doing the same for them where you can.
Don't punish your players for doing well.
A player having a +9 to Perception at an early level really isn't a problem. Sure, starting at level 1 with a 20 in Wisdom and Expertise in Perception is a little minmax-y, but that isn't an issue. The player obviously geared the character towards it, and punishing them by reducing their stats would be incredibly unfair to them, and punishing the rest of the group by making perception checks that are impossible for them unless one player gets lucky is just as unfair.
So, what can you do?
Don't rely on failing Perception checks to make an interesting dungeon.
The secret door? Now it's a magical door. They don't need to roll to see it; instead, they need to determine how to open it.
A tripwire trap? Nope; now it's a giant purple crystal that explodes if the players make too much noise. Instead of rolling to see it, now they have to figure out a way to get the party around it without dying.
An ambush of enemies? Now it's a group of enemies so large or fierce that the party decides they need to avoid the group rather than spot them and kill them.
You can even keep your usual traps, and instead add things in to make them something that requires an approach other than Perception. Keep the tripwire trap, but now the room is covered in magical darkness so they have to dispel that first. Keep the ambush, but now it takes place in an area with heavy fog, so Perception is at disadvantage.
That said, you shouldn't take away success from this player. It would be very un-fun, for both this player and the party, if you took away all Perception checks. She should have situations in which there is an invisible item to spot, or a trap that can be seen. Players have fun when they get to feel cool, and if they've geared themselves towards a large bonus in a skill, let them use it and give them that cool feeling.
Best Answer
I'm not familiar with D&D so this will be a system agnostic answer.
What you could do is provide an in-game explanation as to why the character of the youngest daughter sometimes disappears from the game or does strange things. Give her a character with a chaotic neutral allignment and take over some of the narrative aspects of the game for her.
She could even play a pet (maybe she would like being a big cat?) that's not very loyal and tends to runs off on a whim if she hears a mouse rustling somewhere.
Your youngest will be happy to be included as long as her attention span allows her and the older one will get amusement out of your explanations for the little one's actions.
It would of course be ideal if you could just keep both of their attentions as long as possible, but in my experience nothing is guaranteed to hold a 4 year old's attention for an extended period of time.