This does seem rather fishy. Nina's thoughts about checking in with an elder law attorney are sound. Elders need someone as Power of Attorney, but not just anyone can be trusted with that document. If you feel your mother's being financially (or otherwise) being abused, check with an attorney to see what your next steps can be. It's hard to want to be the caregiver and have your hands tied by something like this.
If you have concerns about the way in which your brother is caring for your mother and about the way in which he is exercising his power of attorney (POA), you might consider contacting the local adult protective services (APS) agency and/or challenging the POA. If you suspect financial exploitation or abuse, reporting your concerns to the APS may prompt an investigation into the ways in which your brother is handling your mother's affairs. The other option of challenging the power of attorney may be a more lengthy and involved approach, and each state has its own laws and procedures on how to go about doing this. It is recommended that you start by contacting the probate court for the county in which the POA was executed to find out the proper procedure. Lastly, you may also consider consulting with a local elderlaw attorney, who may be able to best advise you of your options. To locate such an attorney in your area, you can go to www.naela.org.
I am sorry your Mom has Alzheimer's and that your older brother is being a difficult person. I think there are 2 issues here:
First, the caregiving part. You need to help her to make sure she is clean and safe. This part will have to stay even if your brother says otherwise. This is her right to be well cared for. So you just have to ignore him and continue to help your Mom. If you want to move in, it is fine as long as she has a big house. It would be about your finance and how it relates to Mom's. However, eventually someone with Alzhemer's may need a memory unit later or she will need 24/7 help. You may have to hire a caregiver to help you along the way. My FIL with severe stage of AD had needed 24/7 home care in the end and it was too much for him to be at home, so he is in a nice NH now and he loves it.
Second, the money issue and POA issue. This means your older brother is the problem. Check it out with an attorney in elderly issues and see what right you have. You are the other son so you may be able to come out with some deal iwth the POA. e.g., you are the caregiver. Does the brother also live with Mom? This part is tricky and you may want to be careful. If necessary, you could even go to the court to get guardianship over Mom. You need to be cautious because you may be in more trouble if you fail to get guardianship or more power over Mom.