Greet,
I'm no expert, but if it helps at all, I have a friend who is a cop who says that they have to respond to any complaint, and they have to act oftentimes on very little evidence. He says that once there is evidence of something like that, they have to assume it to be accurate, whether it is or not, that they are not there to decide who is right, just how to handle it for that moment. It's still crazy and stupid that they arrested her, but maybe that helps to understand them a little?
I agree with Ann, I would hire a lawyer ASAP... don't leave this to the government... they will slip up somehow. Get a lawyer, and I would get the lawyer to send her ex a letter stating that if he does not drop the charges immediately, you and your daughter plan to sue him for false arrest, mental anguish, and anything else you can think of. Make the list look long and evil, but make sure it comes from the lawyer, so that he cannot use it as evidence of harrassment. You just might be able to scare him out of going through with this... but then again, I'm not an expert.
I hope everything gets cleared up soon...
*hugs and prayers*