This is something I've had to come to terms with with my dad. He's 77, has bipolar mood disorder, also has some personality disorder issues (schizoid and antisocial personality disorder).
I went through therapy to deal with the emotional issues dealing with my dad has raised, and I would recommend it to you. It helps to have someone objective help you to clear away the emotional baggage so you can deal with the real issues sanely.
The bottom line is that if someone who is a jerk from the get-go becomes old or sick, they are an old or sick jerk. Nobody gets a free pass on bad behavior just because they're old.
You don't need to let your dad's bad behavior pass just because he's old. It's okay to tell him that because of his behavior, you do not want to see him or talk to him or be around him. You can tell him that while you will never allow him to be in want of care, you do not have to visit him or talk to him if he behaves in ways that are hurtful.
That's the route I've taken with my dad. I have obligations to him as a parent that I cannot set aside, but none of those obligations includes letting him hurt me. If he behaves in ways that are mean and hurtful, I can tell him so and then remove myself from his presence without feeling any guilt. I've assured that he gets the care he needs in an assisted living facility.
Do what you need to do to assure your dad has the care he needs, but otherwise don't feel obligated to spend time with him. For your mom's sake, I hope you see her and give her a break from your father's behavior, and I also hope you try to get her to see that she should not tolerate any verbal or emotional abuse from your father.
Think about getting into counseling, it can be a huge load lifted from you to have someone you can talk to about your dad and who can help you deal with the emotional issues.
Hang in there and take care.