should pick All-inclusive - a bit further south to Cancun

Playa del Carmen and Akumal have many all-inclusives - look for those cater for families instead of couples/singles.

Bring some diapers/babyfoods for your first 2 days need so you dont have to scramble to find shops for your immediate needs. Buy the rest at Cancun town but be prepared to pay high prices. Since these are not the usual tourist items, I am not sure you would be able to find them in shopping centers in Hotel Zone.

Also bring your SPF30 Sunscreen - the tropical sun even in Dec is strong.

Buses are very convenient and taxi are reasonable. They accept USD (would be slightly higher than if you pay by Peso).

If you are adventurous, you can even rent a car - the road to Tulum is a straight forward one road. We rented a car for a day in a hotel lobby (not our own hotel, a few doors down at a hotel mainly catering Mexican and Spanish tourists instead of American - much cheaper than from the brand names).

If you want to go to Tulum, I am not sure how suitable it is for little kids... there is really nothing for small kids, only for adults who are interested in history of the Mayan. No shade.