Hmmm...
Belize does sound nice.
I guess the first thing I would look at is with a new baby, what is the health system down there.. If it is more thirdworldish... it would be a big no.
Second, when you say "go to business with"... do you mean that you will be expected to become a partner...and share in the liability of the company, or would you be hired as the operating manager? I would clarify expectations and get something in writing that would exclude you from liability should the restaurant do bad. Also, make sure they show you financials and that it is viable, so you don't waste time/money moving down there and find out it is a bust.
Another thing.. with your DH being a sloper, I know he has to pay for his own tickets from Anchorage - Belize... how much additional is that going to cost you, and will DH's family pick up the tab for that?
I dunno.. first reaction is HECK YA.. ITS BELIZE! But realistically, I probably would say no, but that I would be willing to take elongated vacations and help out with the bar when I was there.