A.,
Our family went with my husbands parents three years ago and we are still talking about our son's allergy chef T.J. He was great! Our son has 7 food intolerances, so he couldn't eat or drink most of the foods in the park, except at the sit-down restaurants.
Breakfast was the most difficult time, so when I contacted Disney about his food intolerances, they made sure we had a fridge in our room (we stayed on property).
The lines will be horrible, especially with three young children. I would suggest to plan on not going on any rides. Take them to Mickey's Toontown Fair. This is where all of the fun children's houses are. There are no lines, and the kids can do almost anything. Water, games, climbing, etc. It's basically a big jungle gym.
Otherwise you might want to go to the park right when it opens if you want to do any of the rides. This way you beat the lines and your kids won't be too fussy waiting. My son and I waited 45 minutes to get on the Dumbo ride. Definitely a long wait for a 3 year-old!
I would really suggest you contact the park (you'll need your reservation number and the dates you will be staying) and talk with one of their food people; they will be able to send you ingredient lists for the foods in the park and give you an idea of what restaurants will be able to cater to your kids.
Here is a good website that you can use to ask a Disney customer service employee your questions:
https://disneyworld.disney.go.com/wdw/contact/contactUs?i...
Otherwise I would suggest your whole family get together for one or two things during the day. Like the African safari would be a fun "ride" for the whole family. And if you get the express pass you don't have to wait in line too long, just get the pass, go somewhere else, and then come back at the appointed time.
This way you can do one group ride a day and meet for dinner every night and talk about your adventures.
Good luck!
-C..
p.s. We found there were not many things to do at Epcot for younger children so we went back to the Disney park for the day.
Also, take a small stroller, the crowds will be really heavy so a big stroller will be too much. But if you have one where another child can stand up (or sit-down on a bench) to rest this would be great. Or plan on lots of rest stops for the kids.