We went to Disney 2 years ago in early April and it was fine, about 80 degrees in Orlando, warm enough for the hotel pool.
WDW: I made reservations for an early dinner at Cinderella Castle way in advance. If you have girls I would definitely recommend it as a splurge. We had friends who did the princess salon, but you can get an inexpensive dress up costume online, put some glittery flats and tights and a tiara in your daypack, and have great pictures. It was by far better food than most of the rest of the food places in the park, a nice air conditioned break from walking too.
The way to save money is 1) drive there 2) don't spend your whole vacation in Orlando! It's the park tickets that make it an expensive vacation. Do one or two theme parks and then save the rest for some other year. 3) Finish your vacation at the beach - Sanibel, Amelia Island, whatever 4) If you get a hotel with a great pool i.e. waterslides and play features, and activities on site like a kid's club, mini-golf and a playground, your kids won't even notice they didn't go to a theme park that day.