My sister lives with my mother. How can we get her out as my mom wishes?

Is it Mother's house? Is Mother competent to make decisions?

If yes to both of those questions, then Mother has to say, "Gertrude, it has been nice having you here, but lately it hasn't been working out so well for me. I really want my privacy and independence back. I would like you to find another place and move out by the end of March."

Then you and other siblings, if any, can volunteer to help her house hunt and pack and move.

If Sister has impairments that make it difficult for her to live on her own, help her get in touch with social services to find out what options might be available to her.

This is so straight-forward that I sense you wouldn't be here asking, if you thought this would work. So tell us, what are the obstacles to making this happen?