As a native New Yorker, I've done this trip very many times via both car and plane. And I would only consider flying. It will be cheaper, faster, and much more pleasant for all. JetBlue is the best option in terms of comfort, though not the cheapest (if that's your main concern.) Countless other carriers do that route as well.
The only exception in my opinion is if you have a large amount of time to spend making the trip; perhaps a week. There are a lot of interesting towns and beautiful natural places between Florida and New York, and stopping for a day or two at many of them would break up the monotony of driving, as well as affording you some nice scenery. I have done this and it was very rewarding and pleasant.
By contrast, the interstate road by which you would drive if you were only interested in getting there the fastest (I95) has no remarkable scenery whatsoever, is poorly maintained in parts, is often subject to large, full-stop traffic jams for no apparent reason, is full of crazy/exhausted drivers swerving between lanes, zealous backwoods traffic cops, overpriced fast food, expensive gas, back pain from remaining sedentary for so long, and the onset of a crushing ennui that will be shaken only by the imbroglio of New York City traffic and consequently finding a place to park therein.
I think you should fly.