Check out the Residence Inn SeaWorld.....it definitely fits your family's needs. We stayed there on our Christmas trip and thought it was great. See my trip report (there's a link in my signature) for lots of photos of the room and common areas (breakfast room, courtyard, pool, hot tub, etc.).
The breakfast buffet is complimentary and very, very expansive for a free inclusion. Hot items change a bit each day so there's some variety.
Internet is free. Parking is free. This is a SeaWorld onsite hotel, so Quick Queue passes are provided free for your entire family, as are shuttles to the SW parks.
Your family would fit into either one or two bedroom suite. Our one bedroom had two queen beds in the bedroom and a queen pullout sofa in the living area. The two bedroom would give a second separate sleeping area and three TV's instead of two.
Each suite has a full kitchen, with a full size fridge, dishwasher, stove, etc.
Front desk staff were GREAT. Breakfast staff were the most pleasant and friendly we have ever met. The hotel was very clean and bright.
The pool is a good size with zero entry. The hot tub is nice and hot but lacks bubbles. There is a sport court onsite for the kids to play basketball. There are barbecues in the courtyard for guest use if you want to 'cue up lunch or dinner. There's a Pizza Hut Express onsite that's much pricer than a regular Pizza Hut but very convenient. There's also a bar by the pool area.
Parking is ample.
There's a CVS Pharmacy just a stone's throw away. If you are getting to the parks by car, its less than 5 minutes to SW.
Let me know if you have any other questions.