Feel like a punching bag, advice?

It sounds like you're being used as the scapegoat in this situation and I would arrange to have some in home care. He sounds like a narcissist who would love to put the blame on you for everything. I would hire someone else to take care of him and keep your distance.

Your father doesn't yell at your husband because he's a man. It's always easier to behave abusively to women or children.
Stop taking all of his calls. Let them go to voicemail. Only call back if you want to. If the complaining and berating starts up tell him plainly that you will not tolerate being spoken to in such a way and hang up on him.
When your out-of-state sister starts voicing her "concerns" tell her to speak with the rehab facility, not you. Go fill out papers at the rehab giving them permission to speak with her instead. Then you can call her with your "concerns" and leave the explaining up to her.
Take a step back. Your father is where he needs to be. Tolerating his berating abuse and asinine nonsense is not going to help anyone, least of all him.
Take a step back and start limiting your contact with him and your sister.

I remember a few years ago when I called my sister as I left my parents house to go home for a few days. I told her that I was tired of driving home crying every single time I departed from my mother. And I said that over and over for the next several years as I continued to be the daughter who helped mom and continued to be on the receiving end of her hateful comments and remarks. Year after year, I took her to her doctors appointments without fail every 2 to 3 months and eventually monthly or more. Her appointments with the specialists were 3 hours from her house and her house was 2.5 hours from mine. The drive time alone was enough to make me tired.
Add emotional abuse to the equation and you can deduct that my mental state was almost to the breaking point and progressing. I stayed the course for 15 years. I raised a teenager in the process, although my daughter's needs always came in second to my parents. If I could change that now as I reflect, I certainly would.
Eventually my mom, who is completely sane and fully aware, drove me to a mental breakdown and I finally walked away from the situation. My sister, who had made it her business to not be available ever, has recently moved closer to my mother. Because I know she is nearer, I have let that be my crutch when I feel guilty or somehow wrong for coming back to my home and going back to work and my own hobbies and projects. I am still adjusting and coping with the bruises, but I am seeing a counselor who helps me maintain my absence from that toxic relationship which continues to be the source of my pain and sorrow.
I often question myself and feel guilt. I have kept my distance for 11 months now and spent Thanksgiving away from my family for the first time in years. I plan to do the same at Christmas.
This holiday has been the most stress-free, comfortable, and non-toxic since my mother was diagnosed with diabetes 20 years ago. Today I feel better. There is a healing that is taking place and it feels way better than feeling abused and beat up day after day and month after month. I can live with this.

yes you are the scapegoat. the calls and visits must stop.
For your health just accept he is declining and his emotions are wild and his venting is his inability to cope with change.
Not your fault. Your choices are out of love and concern'
Sadly older people with issues never see that and vent.
Just stop contact. then revisit it in 3 months and decide if you want to contact him again