Check with the faa website. I had to take medication and was worried about it being liquid over 3oz. I was able to take my prescription liquid medication as well as 4 baby bottles, ice packs, and a few single serve pedialyte bottles. I just had to "declare" it. That just means you have to verbally tell the screeners what it is.
There is a lot of info on the site about traveling with children and passengers with medical needs. You should be able to find the info you need.
Have fun. Disney is totally AWESOME at Christmas!! I did it a few years ago. It's ten times better than going in the summer. Not just the heat. You must see the dancing lights in Hollywood Studios (formerly MGM Studios). I would also suggest the Christmas party at Magic Kingdom if you haven't already gotten tickets. Santa at Downtown Disney's Marketplace was excellent. There's nothing like getting your kids pictures with Santa in shorts!! I'm jealous. My sister is also going in December. Have a great time and good luck with the medical issues.
FYI, I looked up info on hospitals before I went. Just in case. My son is a cardiac patient and was having surgery two weeks after our vacation. Just wanted to be prepared