My aunt is 87 and appears to have dementia, she loses things and accuses others of stealing them, she drinks alcohol a lot, she falls and gets hurt she refuses to get needed surgery (swallowed a key) and when she falls will not go in ambulance to get checked over. I am currently injured (leg) and can not take care of her. How do I get her to a safe place?
In effect, if Mom refuses to continue housing Auntie, then that in itself is a crisis for Auntie. She needs to be somewhere safe and have some services.
Perhaps the right agency to start with would be Adult Protection Services. Mom levels with them. "I love her. I want her safe. But it cannot be in my home. Can you help her? As much as is pains me, I am going to start eviction proceedings."
I am so sorry that the family is in this very hard situation. But Mom does not have to continue in this role. Auntie has rights, but so does Mom.
Re surgery. That, unless she's obviously incompetent (and it doesn't sound as though she is), she has the right to refuse. I would think VERY few doctors would over-rule a patient who refused surgery at 87. The anesthetic alone is very detrimental; much less the risk of infection and the surgery itself.
If your mother chooses, she can re-contact that social worker and simply say, "I can't handle her anymore. She HAS TO GO!" The social worker will take it from there. If she is unwilling to do that? You're just banging your little head against a brick wall.