自己做饭 and Chinese meals? Hesitant to say,

but Cancun is really not a place to do that.

I am not even sure you can find anything more than just a ministore type of shops in the mall at hotel zone. I cannot imagine you take bus to Cancun town and search for a supermarket or grocer to buy your cooking needs.

Cancun really isn't for a family style trip like yours with senior parents and babies.