OP, putting your mom's prior behavior history aside, this is not unusual with dementia and big changes. She cannot adequately process information, and caregivers can seem threatening, etc. Her brain is just not working and while I know you feel terrible and horrified, this is unfortunately an aspect of the disease. So apologize and send a gift, but be sure to speak with the facility to understand what is happening, how she is being helped in the adjustment period, what meds is she on, what precipitated the hair pulling (because your mom may have a trigger) and what steps they are taking to help. Think of it like a toddler who bites at daycare. Of course you are horrified, but the issue is to try to get at the root of the behavior and see if changes can help.
My mother wasn't physically violent with staff when she first entered MC, but she was convinced they were hurting her, when they were gently touching/redirecting, and no "reasoning" will ever work. What did help was time to adjust. medications and a change of facility. I eventually pulled my mother from a facility where the staff was kind of phoning it in, they had a bad ratio of caregivers to residents, they were not education in dementia behaviors, they tended to speak VERY LOUDLY and yell/laugh a lot all of which my mother's brain interpreted as aggressive. The change has been huge. My mother is now in a very small place with very gentle, kind caregivers, and I've instructed them that she does not like to be rushed and she likes to be asked permission to be touched (yes, she has dementia but she is still an individual). She has turned from the suspicious and angry resident claiming people were abusing and terrorizing her (she accused one guy of rape, which was a really huge thing because I'm 99.9 percent sure this was hallucination but we/they had to investigate) to a very sweet, always saying "thank you" and giving/getting hugs from caregivers and being compliant and kind. (and my mom was NOT an angel before dementia). Part of it was that we found the right combination of drugs to help with her agitation, part of it was the time it took for her to adjust, and part was finding the right fit in terms of facility, size, staff training.
I know this is hard, my empathy for the situation you are in, but try to think of it as a problem to be solved and not have your feelings about your mother otherwise get in the way.