More questions -
Will this cause a hardship for you (or your daughter) to go to the more expensive theater?
If you live in an area where most of the "others" have "more" - I can see where some of the choices are more difficult and where saying "no" would be harder.
Overall - a $6 difference isn't (for many) a really big deal. (Especially if I wouldn't have to pay it!)
Shorter driving time would also be a big plus for the more expensive theater.
As others have said - if overall, she's a good kid and relatively reasonable - pick your battles carefully.
Overall - I think I would go for the newer, more expensive theater on this one.
And less driving time would