Well, Miami will be warmer than where you are!
For kids there's the Seaquarium, the Zoo, Parrot Jungle, Monkey Jungle. Might not be beach weather, or you might get lucky! That's in Miami proper. A bit further north there's Ft. Lauderdale. Further south there are the keys. Depends how far you want to drive around, or if you want to drive around.
I enjoy Miami as an adult, but have only ever taken a 16 month old there. I bet if you do some Googling you'll find a few more interesting things to do while you're there. Of course it also depends where else you might have wanted to spend your money on for a family vacation, and whether Miami will be better than that place for your family or not!