Lynn:
If the boys just want to "veg-out" on the beach, a condo on St George Island will be OK. There is a real lack of other things to do and good restuarants if you like to dine out. Apalachicola is an interesting town to spend the day - but a week??
My wife and I traveled all along the panhandle last year in the winter, and found we enjoyed Destin the most. Lots of things to do - museums, nice harbor with fishing/sightseeing excursions, shopping (Bass Pro shop), good lodging, tons of restuarants, world class beach, etc.
The Holiday Inn (right on the beach) - not the Holiday Inn Express - is famous for it's kid friendly programs, but I'm not sure if they will be up and running in March - they have a web site.
You are right on the dividing line between off-season rates. Some of the places keep their low rates through March, others increase them March 1st. Shop around for the best rates.
Hope you have good weather and the boys have fun. I'm sure they will wherever they are as long as they are with their dad!
Jerry