I'm sorry about the situation with your father. It sounds hearbreaking and frustrating.
Has he been diagnosed with a particular type of dementia (Alzheimer's, Lewy Body, etc.)?
Since he has dementia, he might be better off in a memory care facility rather than a regular skilled nursing facility. Have you checked into any of those? They only take patients who have dementia, so they may better equipped to deal with patients like your father.
I really think you need to see an attorney who specializes in estate/elder law. It may cost a bit up front, but can save you an awful lot in the long run, and you'll know you're getting reliable advice.
Did your father give anyone durable power of attorney, medical power of attorney, etc.? A durable power of attorney will give the designated person authority to make financial decisions on your father's behalf. A medical power of attorney does the same with medical decisions, which could address the problem of his refusing medication. Web MD has a good
article about this. (You may know about all of these things -- I apologize if I'm telling you things you're already familiar with.)
If he didn't appoint people in those capacities, though, you will probably have to have the court appoint someone. As you can see, there are a lot of important reasons to see an attorney. You could start out by just making an appointment to discuss your father's circumstances and see what the attorney recommends. There really is too much at stake to trust advice you get from people who aren't lawyers, and the money you spend now could make a huge difference later.
Joining a local Alzheimer's support group could really help you as you go through this with your father. Being in a room with other people who have had or are having similar experiences can help you see that, isolating as it seems, you are definitely not alone. They can give you emotional and practical advice that can help you navigate whatever path your father's disease takes you on.
I hope you'll continue to post here, and let us know how things are going.
Carol