The elderly parent is in skilled nursing - possibly MIS- DiAGNOSED with dementia (Ativan allergy) but the POA is not very pro-active on his mom's behalf. Refuses to transfer POA to his sibling and also refuses to allow his sibling to re-locate his mom to another state where the other sibling can stay on top of things. The parent is being over-sedated and really not getting the care she deserves. Lots of negligence - but everyone passes the buck. We are very worried that if something doesn't change, she will die before her time.
Does the son have both general and medical POA? General POA is typically about financial transactions and not power to decide where the principal lives. But, I suppose, if Brother is in control of paying for the care center, and refuses to pay for a different location, the technicalities may not matter -- the end result is the same. The medical proxy should have decision-making power over drugs, etc. Does Brother have that, too?
I know there are posters here who have gone through the guardianship process and I hope they'll share ballpark costs and how long it took. I understand that a court can decide that the person doesn't need a guardian, or to grant guardianship to the person petitioning for it, or to appoint a non-family member, so it doesn't always result in what the person bringing it to court wants or expects.
I think I'd start with a lawyer specializing in Elder Law and find out all of your options.
I don't see how your brother could transfer the POA to you. He doesn't "own" it and it is not his to give. If you are named in it as the backup and he steps down, then, yes, you'd have POA. But if you are not already on the document, then it is Mother who would have to change it. Is she competent to make such a decision? Does she have periods of being lucid or is she always too drugged to make coherent statements?
I hope you'll get some good background from other posters' experience here, and that you'll find an excellent attorney to help identify the pros and cons of the available options..
What a sad family situation. Not that it is likely to change the answer or the options, but do you have any ideas about why your male cousin is taking the stand he is? If it were just about laziness, the easiest course for him would be to hand off some of the work to his sister.