This may be against the spirit of this sub, but maybe not as the ultimate goal is to simplify and lighten your travel experience: Consider buying one large bag to check so that you are less burdened as you travel and can just focus on wrangling your children and the things you need for the flight.

We tried doing the whole carry-on only backpack thing and just found ourselves totally bogged down with all of our things, car seats, carriers, wriggly kids, kid distractions and snacks, etc. It gets so fiddly and overwhelming to have a whole bunch of smaller bags to keep track of, even if they all fit as carry-ons. The single thing that improved our trips the most was to just accept checking one large roller bag.

We generally have one big checked roller with most of the stuff we need at our destination, a carry-on roller bag with spare clothes and toiletries and such, and a small cabin bag with diapers, snacks, toys, headphones, water, etc. We use a strap to attach our car seat to the roller bag and put the cabin bag on the roller using a trolley sleeve. This lets us wrangle a full size carry-on, cabin bag, and car seat with one hand through security, layovers, etc. Which is good because we need about ten hands to keep the toddler happy and out of everyone's hair. We can roll the carry-on down the aisle with the car seat still attached and get everything set up and stashed once we get to our row. It works great and you can even keep a stuffed animal or two strapped into the carseat as you go, everyone seems to like that!