Hello Dana from Indiana!
So here are my favorites at Downtown Disney that I think your family will enjoy.
Bongos Cuban Cafe: The menu is more friendly to American pallets than one might imagine, and as long as you let them know you want to quieter seating area you will be fine.
Wolfgang Puck Grand Cafe: The dining areas can be a bit noise, but I doubt it would be a problem. This is the most family friendly menu of my recommendations.
Paradiso 37: If your family likes Tex-Mex, this could be a great choice, with a bit more wide ranging menu. Again, ask to be seated away from any live music, in the upper seating area, and you will find it great for all ages.
BOTTOM LINE: Others would add Portobello and Fulton's and maybe even House of Blues to this list, but I think these are your best choices. Of these, Wolfgang Puck's is my top of the list. In any case, ask for seating in a more secluded setting, so as to avoid the noisier settings.
Have a magical (and delicious) vacation!