Only options 1 and 2 make sense--her buying out the mother's share or the heirs share. Letting her stay there rent free for years is only going to delay the sale of the home and the heirs would have to wait for a long time until they got their money.
It is not a good idea to let her be POA unless you trust her to provide receipts and an accounting for any monies she takes out, to be spent on the relative's personal care and NOT on herself. Problem is that once she gets the POA she will be tempted to spend some of it on herself and only way to recover it is for the relatives to sue her for abuse of POA IF your state has such laws.
Who is handling the money now? The professional trust department of a bank could do it if brother is unable to serve as POA. Is there a way to compensate sister for the care she is giving? She sure went to a lot of trouble to try to get this POA!!
DANDY DON IN OKLAHOMA (tiekh@yahoo.com)