One of your questions refers to your father wanting to leave an Alzheimer's unit in continuing care. The other parts of your questions have to do with the family conflicts
about your mom, the distance between you and your parents, and the complex question of his rights versus the decision of the facility to put him in the Alzheimer's unit. Unfortunately, without more specific information, there is a lot of your question that can't be answered here, because the legal authority of the facility and dad's legal capacity to make decisions are not clear. However, one important question is about the extent of his being "a little confused". If he has not been evaluated by a physician or psychologist as to the extent of this problem, that needs to be done. Without objective information available to the family and to the facility, the basis for their decision to "lock him up"is uncertain. Have there been ohter incidents? Did he do something potentially unsafe?
Generally speaking, it is not legal in most places to "lock someone up" unless he is a danger to himself or others. If he is a danger and that is a doctor's decision, your father's rights are determined by the laws of your state, but it is likely that the state will allow the facility to confine someone who is a danger to himself. Wandering and confusion are red flags that warn us of the risk of injury, and vulnerability of an elder to serious danger.
Another problem is the fact that all siblings are at a distance from your parents. I recommend that your hire a competent geriatric care manager to be sure that a proper assessment is done,both of your dad's mental capacity to make decisions and of the appropriateness of his living situation. If you do not know what a care manager can do or how to find the right one, I explain this fully on my website. I have written a short booklet about it. The care manager should be local, know the facility where your parents live, and be responsible to report to one of you. I do hope you have a valid durable power of attorney and a health care directive (also called a proxy in some places) for both parents. You're going to need both of these legal documents.
Next, there is the question of your mom and what the adult kids can do about this conflict, her being "done" caring for dad, and his not wanting to be left by mom. This family matter may lend itself to a family meeting conducted by an experienced professional. I suggest an elder mediator, a geriatric social worker, or someone from the continuing care community who is experienced in assisting with family conflicts. A meeting can take place by conference call, or via Skype over the internet, which we do in my office and other similar professionals may also do. It is important that all family members who are able to be present attend to explore all the possible solutions to this very difficult and complex set of problems you have outlined.
It sounds as if you are worried and that this stressful situation seems to be somewhat beyond your reach. It isn't. A reasoned approach and determination to get to all these issues, one at a time, will help you find your way,but you will need several kinds of help as a family to get there. Seek the guidance you need from the right help. If all the siblings need to pool your resources to do this, it will be worth it.
To summarize, first get an evaluation for dad to see how impaired he is and the recommendation of a doctor about his living situation. Second, use a care manager to be your "boots on the ground" to report to you and to advocate for dad's safety and his desires. Third, find the right person to conduct a family meeting to do some problem solving and planning for the next steps for both your parents.