Is it legal to have a shared POA?

First, I wonder if moving from one house to house to another so frequently is unhealthy, let alone inadvisable, for someone with Alzheimer's. I think this could really cause some confusion, and disorientation.

Beyond that, POAs and DPOAs can be created for joint participation. My father's was, and it would have worked well even though we never needed to use it because my sister and I deferred to each other for our respective roles. She had decades of nursing experience, I had the legal background.

I think the litmus test is whether or not the joint proxies get along and work well together, something only those involved could determine.

A first issue though is whether your/his mother is able to execute legal documents, depending on the state of her Alzheimer's. An attorney would be the best person to create the POA/DPOA, and she/he would speak to your mother privately to make her own assessment of whether or not she understood what she's signing.

If this is your mother's decision, and the three of you work together well, I would get this done sooner rather than later. And raise the issues with the attorney before the meeting, which your/his mother would have to attend, not only for the initial conference but for the document execution after preparation.

Yes. its legal to have joint POAs but I would not recommend it.

No you cannot have a joint POA drawn up because Mom is not competent to assign one. Guardianship would be the next step and that is expensive. I hope you have POA at this point.

"Aside from the difficulties for mom" means your aware that this arrangement is not good for a person suffering from ALZ. It is very hard for someone with a Dementia to be taken out of their comfort zone. Their confusion can get worse. My Mom was ready to leave anywhere we took her within an hour. Then theres the two hour drive. Its a nice gesture on daughters part. You may just want to do a trial run and see how it goes.

I`m not sure what you want to accomplish - POA is a document that has to be made by your mother, and at this point it sounds as though she is no longer capable of that.
This is really an issue that needs to be hashed out between your husband and his sister, whoever currently has POA gets to make decisions, but that does not include the ability to dictate what others must do.