It is great that so many have been able to get through with extended stay tickets. I just know that I will never make that mistake again and it is probably better to be safe rather than sorry when a child is concerned. My husband was also questioned / delayed with his one way ticket to Mexico. He explained that he was returning on a private plane and they reluctantly let him through. The Delta agents practically quoted this material from the State Department's website as they extracted another $300 from me at the gate.

US travelers to Belize need to have a Visa if travel plans extend > 30 days:

http://travel.state.gov/travel/cis_pa_tw/cis/cis_1055.html#entry_requirements