With small kids, I'd try not to bring too many suitcases, I'd just get 2 bigger ones instead of 4-5 individual ones. At some point you may have to move the bags yourself (even with DME, skycab, etc) and moving 5 bags plus carryons plus 3 kids...
You'd have to be an acrobatic juggler to get all that moved on one shot!
When my two kids were little, we could fit their stuff and mine in one large suitcase, with toiletries/extras in hubby's suitcase. Then each girl had a small backpack carryon/tote and I had a small leather backpack style pocketbook. When they got bigger, we had to go to 3 rolling cases, but by then the oldest was able to pull the smaller suitcase. She did that through Heathrow and Gatwick at age 8.

When my two kids were little, we could fit their stuff and mine in one large suitcase, with toiletries/extras in hubby's suitcase. Then each girl had a small backpack carryon/tote and I had a small leather backpack style pocketbook. When they got bigger, we had to go to 3 rolling cases, but by then the oldest was able to pull the smaller suitcase. She did that through Heathrow and Gatwick at age 8.