advice on suitcases for family travel

The one backpack person has a backpack and carry on wheelie bag. The other has a carry on wheelie, one hand free for a kid hand( with kids holding hands. Kids can do their school size backpack for a bit of their stuff

Three main bags should work, as the kids clothes take up less space than adult sizes so one 21" bag should be adequate for the 2 kids.

Just accept that you will be doing laundry

If you don’t think your kids can manage rolling their own small roller bag yet then your plan is fine. Backpack-able adult wears a 21 inch backpack, and can roll a wheeled bag. Other adult has a wheeled bag, and a hands free day bag (backpack or cross body). So that adult has a hand free to hold a child’s hand

My advice if you foresee traveling like this in future years - start teaching your kids to roll a bag. Don’t count on it for this trip - the above plan allows all bags to be managed by an adult. But make one bag “theirs” and encourage them to take turns managing it where reasonable. I can tell you as a parent of only-slightly older kids (8 and 11) that once they can manage their own bag 90% of the time it is so much easier. So much easier, it’s amazing.

Edit - assuming your kids are somewhere near the typical size range for their age, their stuff should easily fit into one shared carry on suitcase. So one bag for their stuff, one for yours and one for the other adult's items (one of the adult's bag is a backpack. You could split it up so heavier things like shoes are in the roller if that makes it easier for the backpack wearer). The kids could also have a small school-type backpack to carry a few toys, books, or light souveniers.

Get a travel vest for yourself , so you aren't carrying a purse. They have inside zipper pockets, and zip up. You are prime pickpocket targets, having to manage luggage and children. Remember Rick was pickpocketed in Paris. Safe travels!

I have traveled with a young daughter. Here are some options for you. Note: 6 & 8 year olds are capable of small, roller bags and smaller backpacks.
1). Get two carry-on Rollers for adults and one medium backpack like an Appenzell. You can get a "duffle" type bag with a trolley strap to attach to top of one carry-on. This way, adults can handle all of luggage independent of kids.
2). Use packing cubes in different colors!
3) an LL Bean book pack 15-16 inches long could be worn by 8 year old.
4). Don't be afraid of a 25" rolling bag. You can manage a bag this size on train and carry along the kid's clothes in it.
5). Try to pack more minimalist. Don't let the kids load-up on toys.

As a single mom who always traveled solo with my kiddo, I have two ideas that may help. I used to take two carry on sized roller bags and we'd each have a personal sized backpack. When rolling through the airports, I'd have the handle up to pull on one, and I'd attach the second to the front of the first bag with a luggage strap. So...one hand to pull luggage, one hand to hold my child's hand. I kept them stacked until we got to the door of the plane and I would unlatch and carry both on with my child herded in front of me down the aisle. Occasionally the top bag would fall to the side and I'd have to readjust, so it was not perfect but usually pretty manageable. If she were still small now, what I would do is get a roller bag that is the size that fits under the seat (15 or 16 inches) and has the trolley sleeve to stack. You and your other adult can have a 21 inch roller with your things, and each have a 15 inch stackable roller for a child, and everyone have their own personal-size backpack. On the way back you can check the 21 inch bags if you like. Hope that helps!!

Edited to add: I just read Sunbaked's post--I like the idea of a duffle or tote with a trolley sleeve to stack too--it would be less weight.

Plan one week's clothes for each person and doing laundry.

Two 21" roller bags + 1 Backpack (Osprey porter 30L or 46L) that can slip onto the carry-on roller bags is more than enough room for everything you'll need, plus you'll each have a personal item if you want to bring more (I'd suggest you not do that, other than one small bag for under the seat for things needed on the flights). With just three bags, you stay mobile and are limiting how much you bring. You wear your heaviest items on the plane and on your train travel days.

I travel a lot with our two kids, often ahead of my husband arriving, or just with the kids if he has to work - we take one spinner carry-on, an Osprey 30L backpack, my purse and each kid has a osprey daylite backpack (13L) for things for on the plane - they're responsible for those packs from start to return, and my older son and I will take turns with the roller bag and backpack, but I usually manage that. We can travel a week or months with just that for the three of us. When my husband joins us, he'll either bring an Osprey 46L or a spinner carry-on, no personal item.