I think you will have a hard time seeing Disney World in 2 days. I’m planning on going in Oct ’07 and will stay a week. Probably with only 2 days (especially with the age of your children) you will do better just sticking to the Magic Kingdom part of Disney World (the girls will love the rides and shows there). There are several low-priced hotels in DW such as the sports themed ones or movie themed. I think they are available for about $85 a night or so. Keep in mind that the rooms are small, but nice pools and decor. Yes, it is easier to stay within DW as you can catch a shuttle bus from your hotel to the entrances to the theme parks, then you don’t have to pay for parking or driving from one park to another.
There is a great book (an unauthorized book) about DW at book stores that is very informative.
Good luck and have fun.