When flying with kids, not checking bags is the way to go.
No baggage check line and no baggage claim wait saves so much time. If you
don’t think you can fit everything, remember that kids get full sized carry-on
bag allotment too, so give them a real bag, not a cute kid-sized bag. Also use
their quart-sized liquids bag to slide your overflow liquids in. Between their
space and yours, you’ll be amazed at what you can fit!