Just choose to eat at the places that have the better choices. For example:
In AK, Tusker house has a chicken leg, mashed potato and applesauce meal.
In MGM, Backlot Express has Chilled Seasoned Chicken with Vegetables - chilled chicken served with carrots, celery, broccoli, and ranch dressing, applesauce and choice of child's size milk, juice or soft drink.
In EPCOT, Yakitori house has Teriyaki Chicken with mixed vegetables, steamed rice and a child size soft drink (my little DD loves the yakitori chicken!!).
In MK, Cosmic Rays has Chicken Noodle Soup served with cheddar crackers, applesauce, and choice of child beverage OR Garden Salad with Chicken served with ranch dressing, cheddar crackers, applesauce and choice of child beverage OR Roasted Chicken Drumsticks - served with mashed potatoes, applesauce and choice of child beverage.
These are just a few quick examples for the counter service places. You can look at the menus for the sit down places and see similar.
One of my little DDs favorites is to get a big fruit cup. There are fruit carts aroung the parks. We got a huge fruit cup (like a parfait cup size) at a fruit stand in AK outside of the Safari entrance. We also got a big fruit cup at MGM in the food area between RNR and ToT. These fruit cups have cut up watermelon, cantaloupe, grapes, honeydoo, etc.
Or you can have your child share an adult meal with you. I can never finish the meal at the sit down places. This is what we usually do. One DD shares with DH and one shares with me. We have never left hungry and we never order an extra appetizer or entree. Sometimes we get dessert if there is one we really want to try.
I have posted some of my kids' meals from WDW on the "Post your disney food pictures here" thread, but here are a few examples:
Kids Steak and mashed potatoes from California Grill
Kids PB&J at Whispering Canyon Cafe
Kids Terriyaki chicken from Yakitori House
Fruit Appetizer from Tempura Kiku
Maggie