I live in Vero Beach.
That time of year is about the coldest weather Florida wise.
We can have beautiful sunny days in the 70s but thats also the time of year we might get our cold fronts too. Its not really a rainy month in general.
As far as the ocean here in Vero Beach in Feb. OK, theres always brave tourists from up North swimming, but in my opinon its not what one dreams of when thinking about a beach vacation.
Another factor that you maybe interested in... we are a very upscale area and where the Disney resort is at is prime ocean front real estate. That time of year all the seasonal snowbird type residents are here so theres alot of traffic.
Vero is a wonderful Disney resort and totally relaxing. The community has little crime, you don't really have to worry about bad areas. Most everyone who visits here wants to come back or at least buy a vacation home here. Its one of the most unique places in Florida. Its more of a family and retiree oriented area. So it would probably be great for your family.
Things start getting more beachy around May. June is really a good month too cause its warm but not super hot yet.