I always pack a carry-on with EVERYTHING I will need for the first 24 hours after I land. I think of it as "flight insurance" in case the airline delays my checked luggage. I may be annoyed that they (hopefully temporarily) lost my luggage, but at least I'll still be vacationing in comfort that first day because I have everything I need.
Stuff for the first 24 hours might sound like a lot, but it's really not. Try it, and you'll see how little space it takes up in a carry-on bag: one complete change of clothes, swimming needs, PJs, toiletries, medications, camera (if not in its own camera bag, which would be considered a "personal item") and a book for the airplane. And remember, each ticketed passenger is entitled to one carry-on bag, so it's not like you have to cram everyone's "24 hour kit" into one carry-on. Last year, my then-5 year old and 2.5 year old LOVED having their own backpacks to take onto the airplane.
Because I always travel this way whenever I fly anyway, the few hours lag in the delivery of DME luggage didn't affect me in the slightest.