April and May are usually just as busy as a the summer months, just with better weather. The problem is with scheduling now in April or May is that dining reservations can be made at 180 days out, and 180 days has passed for those dates. Now, you can schedule early July or late August.
If it's possible, I would actually look into going in late August or sometime in September. While it's a little later than you might like the crowds will be low, it's just the heat that's a concern. Going in August or September would give you plenty of time to plan your dining reservations and make sure you're able to book them in time. Now, if you do still decide to go in April or May you certainly still can scheduling dining reservations, but it will be harder as you might not find any reservations for the day you want or a decent time.
My favorite value resort is POP Century. It's cheap, fun, and it's connected to the other value resort, Art of Animation, so you can walk over there to look at the cool statue!
MY favorite moderate would have to be Port Orleans Riverside, however you might like Port Orleans French Quarter as it's a lot smaller than Riverside.
The dining plan doesn't work for every family, however if you want to do a lot of character meals and would like to have a sit-down, it would be a good option. Plus, everything is paid for up-front and you don't have to worry about paying out of pocket for everything. If your son wants to eat with Mickey, I highly recommend eating at Chef Mickey's. It can be loud, but it's also really fun for kids and you get the meet the Fab Five! Plus, Chef Mickey's is located in the Contemporary Resort, so you can spend some time at the Magic Kingdom, monorail over to the Contemporary, eat, and then monorail back!
If your daughter is really looking to eat with Ariel, I'd look into Akershus, located at the World Showcase in Epcot. It's a princess meal and oftentimes really fun! It doesn't have the same appeal as eating in the Castle but it's cheaper and all the main princesses are there.
Some other places I like to eat are T-Rex (if you stay at one of the Port Orleans resort, you can take a boat to Downtown Disney, where T-Rex is located!) T-Rex can be very loud though, so make sure your children are okay with that. I also like Crystal Palace (which is a must-do for most families!)
My advice would be to have a daily plan, but take it slow and don't try to do everything! Planning can be overwhelming but if you do your research you can really have a great trip. Good luck!