You plan to check three bags and then in addition have three full size rollaboard bags and three back packs? You hope to gate check the rollabord bags for free?

I travel with family a lot, kids included. Honestly if I travelled with as much stuff as you plan to I would give up travel today.

If you plan to check a bag each, I assume a full size suitcase, then you have no need for a rollaboard bag at all. Take a back pack each with the essentials and then you can be 100% certain it will go under the seat in front of you, or in the overhead if there is space.

Unless you are actually relocating there is just no need to take so much stuff. A young child and a man should easily be able to share a regular suitcase. How many outfits does one human need?