My only response to this fraternity would be "who the hell do you think you are??!?"
Telling your sisters to be ready for a mixer in half an hour...the nerve. I would tell them to take a flying @#*% through a rolling doughnut. We NEVER had an unplanned mixer like this, and would have probably not even communicated any further with a fraternity that made such a rude request.
Now on the other hand, we hung out with Crows all the time, and there would be times when they'd call the house and say "we have a keg if any of you guys want to come down." That was completely different - it was not a mixer or official event.
Tell them you DO NOT operate this way and if they want to mix with you, it must be scheduled. If they won't do something as simple as that, I don't think you're missing anything by not associating with them. They sound like arrogant jerks to me.