There are plenty of options in the parks. You just have to think ahead. Besides kid menus, there's always the sharing option. You can pack along the snacks mentioned already. Depending on which resort, the gift shop may have a take-away cafe in the giftshop. The Beach Club, for example serves eggs, etc, out of there's.
My favorite restaurants in the parks are The Rose & Crown and Marrakesh at Epcot. The fast-food moroccan place is very good as well. They also have turkey legs at the American pavilion, and the french boulangerie generally has a cheese plate.
At the magic kingdom, we usually eat casually and get salads at the place in Tommorrowland. There are also turkey legs in Frontiereland.
At Hollywood studios, there are turkeylegs at the stand on the way to the Rockin Roller coaster. The food at the brown derby is meh and very pricy. The casual place next to honey I shrunk the kids has burgers and not much else.
I've only been to Animal Kingdom once, and after we found the bar in the middle, we didn't eat much...
In downtown Disney, avoid Wolfgang puck's. It's way overrated. House of blues is good for low-carb, as is fultons crab house and actually Raglan Road. Raglan Road has a braised lamb shank to die for. I like Bongos, but I haven't tried to low-carb there. Rainforest Cafe might work as well, we just don't go there often.
In the resorts... Wilderness lodge has a very fun restaurant with interactive servers and all you can ear BBQ at your table. Theres a steakhouse at the Yacht Club which is right out the back gates of Epcot. Ft wilderness has Mickeys hoedown.
Hope that helps. I'm on my phone, it's a little hard to post more. I'm a Disney wife, and we have been most places in the parks.
Carolyn (32 lbs lost Pre-op) HW: 291, SW: 259, GW: 129.5, CW: 126.4
Age: 45, Height: 5'2 1/4" , Stretch Goal: 122