If they felt they really had to arrest her they should have left the mother to calm her down and asked her to bring her in the next day, there was no need to do it the way they did.
At that point they would also have looked at the body cam footage, agreed whether what was said was homophobic or a misunderstanding, found a correct crime to charge her with (I have read that a public order offense cannot be one that happens in a private residence and it also has to be reported by a member of the public but IANAL) and sorted this all out without all the violence.
I think the officer involved needs to be investigated for her homophobic attitude, saying someone looks like a lesbian you know is not an insult, but this does depend on what she thinks she heard, at the very least she needs disability training, anger management and a removal from frontline policing until she learns how to behave, deescalate, not jump t conclusions and not abuse her position. She also needs to be arrested for assaulting the mother, unlawfully entering their home and possibly assaulting the daughter.
It's all appalling but unfortunately not surprising. I was told by a domestic abuse police officer that someone with autism is more likely the abuser in a domestic violence situation when ALL evidence points the other way, they are more likely to be the victim. What hope is there when the people whose job it is to protect you are under the impression that you are more likely to be violent due to your disability?