We were allowed milkshakes for the kids drinks, but beware as the kids dessert is ice cream (you will find most of the TS places are ice cream for kids) so that was a lot of ice cream that day for them, they were not complaining though!!
We were NOT allowed anything but sodas at Tepanyaki, I would not go to the place again BTW...no lobster...appetizer was a SMALL TINY salad...like 1/2 c salad...and we were told BEFORE we even ordered, nothing but sodas and NO LOBSTER...also nothing for desert except ICE CREAM (even for adults) even though they have another desert menu...
with all the unique places is WDW, I will try another place at EPCOT next time.
At CM we were allowed shakes(kind of icy, not creamy or smooth) and smoothies (good but tart for little kids my dd said) and our waiter told us up front we could order any kind of beverages off the menu non alchoholic...he was really nice
the Sci fi waiter was helpful too...
Captain Cooks at the Poly was VERY VERY generous with credits and they have a LONG list for you to look at if you are confused over what counts for what BTW...the lady INSISTED I take a desert
I like that kind of service actually...she said I should get my monies worth!
I have read of some people getting poweraides with snack credits, at the parks we were not allowed to do this, I wonder if the resorts are more liberal with credits??