the paradise is a nice ship, but imo if your kids had a good time on another ship, they may be disappointed (and bored) on paradise. It does not have the bells and whistles of the newer ships, by any stretch of the imagination.
This is fine for many people (including DW and I), but the design dates back to 1989-1990 if I remember right. If you are looking for a 'family friendly' atmosphere with lots of stuff for your kids to do, it isnt here. If a 4 day cruise is what you are looking at, the Royal Caribbean Freedom class (Freedom of the seas , Independence of the seas, liberty of the seas) and voyager class (Mariner / Explorer / Adventure of the seas) will likely be more to your (and their) liking.
I *will* say that IMO Carnival has better food, but RC has carnival beat in the activities in short cruises department.