My dd almost 5 and I went in mid april and had a great time. Get to the parks when they open, (actually 1/2 hour before) know What you want to do for the first three or four things and off you go. you can do a lot of rides early without waiting in lines.
We ended up renting a stroller for my almost 5 year old. (her choice) and it helped a lot. She never uses one at home anymore (we don';t even still own one) but it make getting around easier she could rest and faster, since I can go faster strollering her. If you rent, take a cheap scarf (I got one for 94cents at walmart) and tie it to the handle. It makes it easy to spot and no one messes with it.
Playhouse disney was fun, and so was the snow white show.
We stayed at the DLH and she loved the fish ponds and remote control boats. (see our trip reports, mom and abby's great adventure)
Just remember to pace yourselves and not try to do too much in one day or everyone will get cranky. We would leave mid day and go back to the room and rest and/or swim. Also, eat before the little ones are starving. (I always push this one, and she is starving and cranky)
have a great trip.