Psychiatric vs Dementia, any input?

It sounds like the other resident would benefit from a geriatric stay at a hospital. Some MC facilities require this before admission. It was required for my mother. It’s hard b/c dementia patients go through delirium or stress being moved to a new environment but this resident sounds very agitated. If its been going on for weeks it needs to be addressed. I would reach out to your local Obundsman too and ask what to do? They might provide some insite or be an advocate for your mother in a way. Good luck! I see all sides of this and feel for you and the family with the very stressed out dementia loved one.

Geaton77 is right. Your MIL is not the one who should be moved. Neither should any of the other residents who are getting along just fine.
Memory Care is not the right kind of care facility for what sounds to me like a paranoid psychotic who also has dementia. I'm not a psychiatrist but I do know that a memory care facility does not have the kind of staff or security that's needed to keep all the residents and staff safe from a patient like this. People often think an elder with dementia is only a risk to themselves. That's not true.
I know of an incident in a nursing home and MC facility where an elderly resident strangles his elderly girlfriend (also a resident) to death because he thought she was "cheating" on him with someone else.
This happened at an Autumn Lake brand care facility in Connecticut. I believe in the town of Waterbury. Find it online and show it to the Director of the memory care facility your MIL is in.
Then ask him/her if the facility would be prepared to pay out millions of dollars in damages when the violent, deranged, demented lunatic who does not belong there among the other residents, actually hurts someone. Inquire to the Director if a brand-new facility with only a handful of residents carries the amount of liability insurance and retains the number of lawyers a multi-million dollar nursing home chain does.
This is the only way you're going to get any action from the administration of your MIL's facility. They will continue to skirt around your concerns and will do nothing about the resident.
Show them the Autumn Lake story and ask the questions I put here, and I'd wager there will be an ambulance showing up to take that resident away to a hospital before the day is done.

I think the answer to your question is "both psychiatric and dementia".The new resident is experiencing psychosis (beliefs inconsistent with reality) that are terrifying to her. Ordinary measures have not helped. A memory care does not have staff or skills to help her. An inpatient locked psychiatric unit (ideally a geriatric psychiatry unit) is the right level of care.
So there is a place for her to get what she needs...though it is not your problem to solve. Being clear about impact of your mom and your serious consideration of moving her so that she does not become angry/exhausted by the situation is the point to make clear to MC director, facility wellness nurse, facility administrator, etc. And if you and your family can visit often and take mom out of memory care to another part of facility to visit, or out of facility for a couple of hours, that will give your mom a break from the situation and help her to cope until there is some resolution.

The women's actions are from the Dementia. It takes up to a month to see if a med will work. If it doesn't, then they try another one.

IMO, the woman needs a psychic facility were they can try her on different meds till they find the right cocktail. MC is not where she should be. Not enough staff to deal with this. I would wonder who is prescribing the med, a GP or a Neurologist? It should be a Neurologist.

You need to approach the Director calmly. Explain that Mom wants to move because this resident stresses her out and she gets agitated. Then say you really don't want to do this because Mom did like it there and you felt she thrived. Can they not do skmething for this woman like send her out for a psychic eval. Its not good for this resident to have this much anxiety either.

Your MIL is not the one that should be moved. She was there prior to the disruptive resident. It is unacceptable and the admin there needs to address it or this resident needs to be removed until her behaviors are addressed. Why should 1 person chase everyone else out? No. Keep the pressure on until there is an acceptable solution. Ugh...I'm so sorry you're dealing with this. May you get resolution, and soon.