The park's food is OK. They have several dining options including a restaurant right on the beach (see the special report on Chankanaab at http://www.caribbeanportreviews.com/...Chankanaab.htm
It should answer your questions. Also, you can take a taxi to town for Carlos and Charlies and then return to Chananaab with no problem. It would be $10 each way.
However, after you enter Carlos and Charlies, it is unlikely you will return to Chankanaab (or anywhere else, for that matter). VBG
Have a great day in Cozumel.