He at times drinks heavily. He is also not well himself. He refuses to let my mom come live with us. My brother and I are devastated. He also refuses to let us be part of her doctors appointments or even talk to her doctors. He is not very patient with my mom. I cry every knowing she is in her care. I know I can do a better job caring for her. It is important to me to care for my mom and to have her remember me. What can I do about this without it getting ugly. He makes it very difficult and often gets very verbally abusive and nasty. I can't stand him. He literally keeps my brother and I at arms distance with my mom.
I don't see how it can't "not get ugly", and I think you have to prepare yourself for that, based on your description of your father's behavior and that fact that you can't stand him.
You could call Adult Protection Services (APS) and ask that they do a well call.
It might be possible that you could get Guardianship of your mother but this may be difficult. You may have to prove neglect or abuse.
And you can forget about not wanting this to "get ugly" cuz it will.