Mom needs assisted care due to stroke & Parkinson's, Dad refuses help for her. Anyone else been through this?

Also, please realize that dad doesn't get to decide what mom gets or not. It's not 1956 anymore. YOU have to decide what's good for mom. You can do it. We all have been through this and will support you.

Time to be the adult here.
What dad wants is not what's safe or good for dad. Or mom.

If their need level is similar, you may be able to find a double they can both live in together. Or at least on the same campus. A lot of married couples are moving into "independent living" apartments, and transitioning into other units as their care levels increase. You can bring furniture from home.

A difference is they won't be isolated at home, watching TV all day. There are activities, outings, and a lot of services come on site vs them having to go out. My mom's place had visiting doctors who saw her in her apartment. They could do everything but imaging. Onsite PT, dentist, post office, gift shop, barber/beauty, dining room.

As mom's dementia advanced, she simply transitioned into other units on the same campus.

My advice is to put them in a place that can handle the next stage of need, not what they need today. Things change so quickly you don't want to be looking for another place for them in 3-6 months.

Some level of guile is required to do this. You can't just blast them with "you're not safe anymore and you have to move." You many need the doctor to tell dad it's time for change, for mom's sake. Most elders will listen to an authority figure who can appeal to their ego. Unless reasoning is farther gone than that. If so, you may just need to do what you have to do. They won't stay mad at you forever.

You cannot reason with dementia. On the other hand, you can redirect it. Would Dad be willing to give it a try for a month? We took mom on tours of facilities. She liked the idea there were activities and bus trips and three meals a day that someone else cooked. She did a one month trial at half price, just packed like she was going on a cruise. I don't know where you can get a one month cruise for $1200. She did this in March, and she had a bad case of winter cabin fever at home. She loved it, she stayed. She didn't want to live with old people either, but she quickly forgot that when she reconnected with friends from high school.