I wouldn't do Tikal with kids so young as it is a very long day & they wouldn't get much out of it, possibly the same for Caracol. But you could do one of the closer ruins like Altun Ha or Lamanai. The zoo is a good idea with kids. Are you staying all on the island or splitting it up and staying part on the island, part on the mainland (where the ruins & zoo are)? Any of the day trips from the island would be a long day but enjoyable with boat ride to the mainland, etc. Be sure to bring juices, diapers and anything you will need since not a lot is available on the tours. Probably a kid carrying backpack would be the way to go with the 7 month old as strollers would not be very manageable either on the island or on the tours.
No shots needed - just bring a good kid safe bug spray.