Is there a large selection of rental homes once my family moves there?

Depends on your price range...

VRBO.com or Flipkey.com are fantastic for finding rental homes.
also the classifieds on sanpedrosun.com have short and long term rentals often.
some people also will post their rental availability here but nothing consistent.

It will all depend on:

• How many people/bedrooms/bathrooms needed
• Lagoon or ocean side
• North, Central, or South of town
• Amenities you require (AC? Wifi? a Pool?)
• Length of stay and time of year for travel

They appear to be talking about rentals once they've moved here - flipkey and vrbo won't work as they're for short term holiday letting.

Plenty of long term lets but need to be on the ground generally. See the lodging section of this site has a Long term section with Agents and will give you an idea of the range

Oh Lord not this question again! Is your family moving to AC or Caye Caulker? Are you aware they are different places?

From the question it seems as though you've never been.Have you?

I would have my doubts.

I am always amazed when people plan to move here that have never been here. That rarely,if ever ends well...

I don't live there but have visited many times starting with my first trip in 1991 up to my last trip in March and I too am somewhat amazed. Some people expect it to be the way it was in 1991 (not even close) and others think it is too primitive now. (What, no Wal-Mart, McDonalds or NFL franchise!)
I would say live and learn but unprepared people can sometimes burden others.