Traveling with young children is way different from traveling solo. Your 4 & 7yo could wander off in different directions simultaneously and get into trouble quickly. You don't want to be weighed down by bags when you have to watch and chase them. Plus, at some point you'll have to carry the younger one instead of a bag. My advice is carry on only what will be necessary in flight or within hours of arrival -- note with two young kids that could be A LOT (toys, medicine, jackets, 1-2 changes of clothes) all by itself -- and check absolutely everything else.
Bon voyage!