Caregiving is not for everyone for whatever reason. Just make other arrangements; you want Mom safe and well cared for but that does not mean anyone has to give up their own emotional or physical wellbeing.
Not to be harsh, but why do you expect your sister to care for your Mother?
You are beating a dead horse. She is not capable of being a caregiver, she is a Blank. In basic training for any uniformed service, there are trainees who just go blank at a moment of extreme pressure. You go blank, you go home. You do NOT want this type of person watching over an elder person, because if the elder faints and falls, the Blank will freeze or just scream. They won't even have enough sense to call 911. Trust me, I know, you don't want them involved, for the safety of the patient.
I take it that you have different mothers, as you refer to your sisters mother as "her mother" and not "our mother". In any case, I would suggest that her mother be put in a nursing home, where her mother's assets will be spent to take care of her, as they should be, instead of going to her daughter, who is just waiting for her die.
Unfortunately, this is very common. Adult children of aging parents that do not help with caregiving, resurface with lightening speed when it is time to collect the inheritance. Since you feel you would have to force your sister to help with your mother, perhaps your sister does not appreciate your mother, and it may be in the best interest of your mother not to have your sister help her. Possibly your sister should ask herself why she thinks she even deserves an inheritance since she is not willing to help her mother.
rob2lob, does your sister believe that Mom should be in a memory care facility? Sometimes siblings can see the forest for the trees, yet the Caregiving sibling keeps digging in their heels not wanting to let Mom go.
As as the others above have mentioned, not everyone is cut out to be a Caregiver. No different than not everyone is cut out to be a brain surgeon, or an attorney, or a CEO of a large corporation. We all aren't cut from the same cloth.
Does she have POA? If not, then she's not responsible for taking care of mom. Period. My sister is POA, but I've been "forced" by circumstances to care for mom. It's now beyond the point where I can safely manage it, and I have no recourse or resources. So there is a way to "force" the care on her, but it won't work in the long run. If you are POA, get your mom to a safe place, either your home or assisted living and don't expect your sister to help with anything. She sounds like the typical good-for-nothing sibling. Don't forget to remind sister that when mom is gone, all that "inheritance" will be gone, too, spent on taking care of mom, as it should be.
You can't force someone to be a caregiver.
Not to be harsh, but why do you expect your sister to care for your Mother?
How bad is your mother's Alzheimer's? Has she reached the stage where one person is not enough for her safety and care?
Are you your mom's durable and medical POA? Does she have assets that can be used to pay for her to have some extra caregivers?
Does your mom have a living will and a regular Will?
You do NOT want this type of person watching over an elder person, because if the elder faints and falls, the Blank will freeze or just scream. They won't even have enough sense to call 911. Trust me, I know, you don't want them involved, for the safety of the patient.
As as the others above have mentioned, not everyone is cut out to be a Caregiver. No different than not everyone is cut out to be a brain surgeon, or an attorney, or a CEO of a large corporation. We all aren't cut from the same cloth.
You cannot force an adult to do anything. If you think her mother is being neglected, reporting it to APS is an option.