We have 2 children, boy and girl (8 &10) We got two connecting partial gulf view rooms, one king/1 with 2 queens, so that we could have 2 baths. The rooms are small, but well laid out with the desk and entertainment center and closet all built in to one wall. The furnishings are better than the Grand Floridian, but the rooms are smaller. The hotel is very old, so I've been told that the rooms vary in size. Not sure how many children you have and how long you will be there, but you may want to get 2 rooms, or consider the beach house suites. Quite frankly one room for a week would get cramped, but it depends how much you stay in your room. We are usually at the beach all day long.
Every year I try to get the kids to go to the children's activities, but they always want to stay with us, and we also have family reunions with lots of cousins to play with. I'm afraid I can't be much help on that.
You will feel very comfortable with children. In fact, the pools are filled with them! Don't miss the ice cream shop/candy shop in the hotel. We always reserve beach cabanas (I think they were $15/day) for some shade. The pool bar serves breakfast also, so we usually ate outside every morning. They also have free coffee/tea in the lobby in the morning. They will bring food and nonalcohol drinks to the beach, but St. Pete has a local ordinance forbidding alcohol at the beach. But you can bring it down yourself. Their drinks are super!
There are plenty of beach towels at the pool and they offer ice water as well. They used to have noodles and kickboards, but I don't remember seeing them last year.
This summer we are doing another family reunion and we have reserved a two bedroom suite (it was cheaper than the two connecting gulf front rooms). They offer some good packages though.
We have never really eaten dinner there, because we always go out to other places that are more casual. There is a place in St. Pete' Beach called Ted Peters that has excellent smoked fish as well as great burgers. There are plenty of places to eat. Hope you enjoy it.