Should I install a hidden camera?

This is a tough one. As you have already observed her pinching him, what will you do if you see more of it on camera? Perhaps you should get the advice of an attorney. If you annoy her and she takes her own action you might have a larger problem. What about her mental health? Does she have children? Perhaps you can tell her you would like to have a father and daughter date. That you would just like to have a little time alone with him on a regular basis. Tell her this will give her a little time on her own. Do you attend his dr appointments? Invite yourself along if not. As DPOA Do you have both medical and financial? I know it must be hard to see him in what might be an abusive relationship. I'm afraid I would call her out on it in a nice way but in a way that put her on notice. But that might not be what your dad wants. There is a fine line. My niece went through a bit of this with her FIL. Married a woman who hadn't been married in 35 years. They soon discovered why. Very stressful. When the FIL passed, it took quite a while to get his wife refocused on her own grown children instead of niece who had been paying their bills etc.
Let us know how it goes.

The nurse said she had noticed that the previous "sweetness" of her towards him had disappeared. Our family has watched her pinch him, hit him in the arms, which in a younger person might not leave a mark, but because he IS old, does leave a mark. I have personally seen him rub his arms after one of these hits. I understand it's not what she thought she signed up for, but he was already in the throws of dementia when they met and it was obvious. My dad also takes no medications, so no blood thinners or other kinds of pharmaceuticals.

absolutely! I had cameras and they were life savers! IN my State I could have audio or video and I chose video, all States are different. You wouldn't believe how such sweet people are NOT!

PNW, I noticed you wrote "I suspect".   Do you have any hard evidence that any type of abuse is going on?   Have any of the Staff noticed anything out of the ordinary?

This is tough, not only for your Dad, but also for his wife, especially since they have been married only 4 years.   My gosh, I bet they never thought this would be how retirement would be.   Being that the wife doesn't want him out of her sight means she is scared about the future.   And also angry that this has happened to him.   Plus in denial regarding how much care he needs.   You need to put yourself into her shoes.

I wouldn't do a camera.   That might cause the wife to pack up and leave, and your Dad would be lost without his wife, as with dementia one depends more on their spouse to give routine to a day.

As for physical abuse, falling can become very common with dementia, thus the bumps and black/blue marks.   Aging will also cause one's skin to become thin thus a tiny light bump can make it black and blue.   More so if one is taking a blood thinner. 

So there is a lot to think about.

Maybe the wife needs more time away from her husband. Ask the nurse if she thinks it's just that or if she thinks it's abuse. Would the nurse tell Adult protective services what she has seen if you need to call them?

Laws vary by state but all are pretty consistent about video and audio taping without knowledge and consent anywhere where a person has an expectation of privacy. That would include their home or a private room in your home (bedroom, bathroom)

I wasn't insinuating that his bad haircut was a sign of abuse or neglect, just an observation. He is certified by two board certified physicians to be incapable of handling his own affairs. I am MOST concerned about her and the noticeable meanness towards him, which the nurse has noticed as well.

First off, it is an invasion of their privacy. Second, your allegation of a bad haircut as abuse or neglect would be laughed right out of court. Your DPOA allows you to carry out his wishes. If he expresses the need to separate, by all means rescue him with the help of an attorney. If he does not want to leave, stay out of it.