Mexican grocery stores are cool and easy, super fun for your kids too. Relax and get out of the resort, it'll be a good experience for the family.
Buy a ton of eggs and cheese, etc. and this is not a week to go low-fruit! Steaks are really good and cheap in mexico as well as fruits and basic veg of course. I'd buy a huge mound of beef fajitas (w/corn tortillas) ingredients and a huge ton of eggs and salsa, and cook several easy mexican meals at your place. I did exactly that this summer, it was easy, fun, and saved a ton of cash and time.