I know they can do something at 50s PT. I got a PB&J shake to go. They might be able to help you out with a scoop to go if you explain the situation. (Also did a DF milkshake at Sci-Fi but that doesn't have the walk/in bar setup that they have at Tune In.)
Also, outside of the parks, Beaches and Cream can help you.
I know those aren't really what you are looking for (CSes) but perhaps it's a resource if you get totally stuck
ETA: There is a place at AK with ice cream - I don't know for sure but I'd bet you can get some there. It's back in Dinoland, next to Restaurantosaurus. If you are facing Rsaurus, it is to the right, with the Boneyard behind you, in a trailer-looking building. Kind of in the corner. Sorry for the stinktastic description, hopefully it makes sense.
ETA2: Dino Bite Snacks! Also, per an older thread, Dino Bite does carry it. In EPCOT, Liberty Inn and Hollywood Scoops in DHS are listed as having dairy-free ice cream. I haven't eaten there to verify, though. But I sympathize with your DD, I am an ice cream ADDICT and it's one of the foods that causes me to be most symptomatic with this new dairy allergy... second only to straight-up milk.
