I think Chichen Itza might be too long a trip for your baby

And that is the most visited Maya ruin site on Yucanta Pinninsula, also a world heritage site I believe. As I recall, it was a long day trip in hot steamy jungle weather. I went in October and the weather was very unpredictable. We experienced very sudden pouring rain on a bright sunny day.

If you stay in the hotel zone of Cancun, there is a shopping mall in the center of the hotel zone, not sure baby stuff is sold there. Otherwise, bus rides to the real Cancun outside the hotel zone are very easy. We took the local bus and ferry (to Cozumel and Isla Mujeres) a few times while there and even a long distance mexican bus to Playa Del Carmen. Very few non-Mexican tourists on these local buses and ferries. We found them mostly clean and safe. And we had more fun/flexibility than the tours designed for the tourists.

As I recall, there was at least one all-inclusive resort on the far end of the Cancun hotel zone. By the way, the hotel zone is located on a strip of narrow land with water on both sides - one side being the Atlantic Ocean of course. There is a small Maya ruin in the hotel zone.