I handle it by saying, "Excuse me - the line starts behind me." If five girls with big attitudes cut in front of me, I'm not sure I'd say anything, either, though. I don't want to get swarmed. I'd certainly back somebody else up who was willing to go toe-to-toe, though.
This sounds kind of funny, though - "Since she is pretty scared of rollercoasters, and stressed out about the heat and was also on her period at the time I figured we should just drop it and not let it ruin our experience." Doesn't sound like your girlfriend's having a great time anyway.