Thatch Caye welcomes families and young children. I am the manager and my wife and I have a two year old baby and one on the way. There are often other kids out here too, since the workers can bring their kids out for weekends to visit.The workers here all have lots of experience with kids and know how to babysit them and keep them occupied. We don't mind getting a worker to help babysit if needed as long as we know ahead of time what to expect. We don't have beaches like Cayman or Cancun but we do have small beaches, lots of kayaks, and several great swimming and snorkelling areas around the caye.
October is not the best month to visit Belize yet it is actually better than December and January a lot of the time. October can be a rainy month (but we have close to a six month rainy season here, so it's hit or miss on that one most of the time) and October is pretty much the peak of hurricane activity in the western Caribbean. If anything is brewing nearby, Belize will probably get some effect even if it is just a lack of trade wind breeze from a hurricane somewhere else stealing all of our air. That is also why October can sometimes get a little buggy. But December and January give us cold fronts that are nothing like what one thinks of when one envisions the sunny Caribbean. They turn the sky a dreary grey color that lasts for several days and often the seas get very rough and the temperatures get into the low 70's which is fine for people coming from a deep winter, but is marginal for tropical weather lovers.
So, to sum up, expect some rain showers and not as much breeze as other months, but also expect nice warm temperatures (the sea is like bath water during October here). Visibility is good then, but not as good as the dry season months, although at least 60 to 70 foot visibility can be expected in October and often more than that. Atoll trips can be done from San Pedro, Caye Caulker, and right here at Thatch Caye. I also think that most atoll resorts don't have age limitations, but since they are all heavy diving and fishing operations out there, they also don't have much to do for kids so they get bored easily.