Hello Jamie!
You ask a great question! If you are looking for a Quick Service Meal in Disney's Hollywood Studios, I would recommend Starring Rolls. They offer a great Ham or Turkey Sandwich, along with some healthy side items. I am not sure if your three year old likes peanut butter and jelly sandwiches, but these are also available at Starring Rolls.
There is a great Unofficial Walt Disney World food blog called The Disney Food Blog that has listed some other healthy Quick Service Options located at other Disney Theme Parks:
* Sunshine Seasons, Epcot: Soups, Salads, Noodle Bowls with Stir-fried Veggies, Roasted Meats
* Cosmic Ray’s, Magic Kingdom: Turkey and Bacon Wrap, Veggie Wrap/Burger
* Sleepy Hollow, Magic Kingdom: Chicken and Rice Soup
* Tomorrowland Terrace Noodle Station, Magic Kingdom: Steamed Broccoli, Noodle Bowls
* Tamu Tamu, Animal Kingdom: Tuna salad pita, Turkey and Swiss on Focaccia
* Flame Tree BBQ, Animal Kingdom: Turkey sandwich
NOTE: These options are only offered on the adult menu. Please keep in mind that with the Disney Dining Plan, your kids will only be able to order from the kid's menu. I will say there are more healthy side item choices than main entree choices on the Kids' Picks menu. However, if you want your kids to have a larger entree choice, then I would not recommend the Disney Dining Plan.
I hope this answers your question. If you have other questions, please let me know!
Have a MAGICAL day!
Wes