Not sure how big or small that tight budget is but I think you might be well served by checking into some of the many timeshare resorts, as the PP suggests, in the Disney area.
For pools and childrens' activities I'd suggest (in no particular order of preference) the Sheraton Vistana Resort, Marriott's Cypress Harbour, Marriott's Grande Vista, Marriott's Harbour Lake, or the tri-Marriotts adjacent to the Marriott World Center Hotel property - Imperial Palm Villas, Sabal Palms or Royal Palms, Orange Lake Country Club Resort, or one of the three Hilton Grand Vacation Club properties (SeaWorld, International Drive or the new Parc Soleil resort). Renting from a timeshare owner is usually a less expensive option to making a direct reservation. Check out
www.redweek.com or the classifieds at the Timeshare Users' Group site
www.tug2.net.
As for standard hotels, the Marriott World Center hotel's facilities are pretty impressive - several pools, water slide, game room, large food court, a childrens' activity center and the long list of planned daily childrens' activities.
Dick Taylor