I am really sorry. I can identify on some level with some of the things you wrote and the situation you are in. Its very difficult.
I agree with the above poster that you are not your dad's keeper though. And that you are not responsible for his actions/behaviour.
I know that knowing he behaved /s like this hurts you and you feel he betrayed you and your mother. That may be true or may be true to an extent.
I think it would be useful to talk to him quitely when you both have the time. Listen to how he sees this, what he feels and why he is acting the way he does and express your concerns, hurt and disappointment etc...
I am with you on the loyalty front etc. But there may be a way you can see how things are for him and that would make it easier. Maybe not...
In any case - for your sake and your mother's sake I think the rational thing to do is to stay in touch. You need to be aware of what his decisions are and how it affects her. He needs to know what your priorities are and respect them. I do not think that he should be the only one deciding where your mother should be (given your age
I know some one (a distant relative) who put his wife in an old people's home because she does not communicate or knows where she is but some times knows alot more than others... some times she recognises people and some times she doesnt. I know its hard on her husband. They have a carer as well looking after her and he comes to see he {ONLY} 3 times a week. Its beyond me. Where is the care? the love? the compasion? the responsibility and loyalty for the one you love. It breaks my heart every time I think about this. And I know she loves him so much. She adores him.
You have to go beyond your feelings and possible anger and make sure you stay close to look after your mother.
I do hope she gets better and I wish you the very best!!