What's the right thing to do in your heart of hearts? In the place where you're protected from the anger and expectations of others, the place where if everything was honest and good and you are free to do what you believe to be the right thing, what would you do?
This answer is based on the possibly completely wrong assumption that your father has Narcissistic Personality Disorder. It's not necessarily as bad as it sounds. People with NPD can be charming, funny, fun to be with people. Or they can be very difficult. Or both. There are actually five subgroupssubtypes of NPD in the DSM-5, and how a narcissist behaves depends on the specific group they're in. So. Take this with whatever caveat is applicable.
Because interpersonal skills with a person who cannot relate to other people in an empathetic manner don't matter, I'm not going to navigate a fine line. Setting boundaries won't work. Sincere conversations won't work. Explanations won't work, so advising this tack would be, well, in my opinion bad advice.
Your father will blame you, yes, and there will be no reasoning with him, because Narcissists are never wrong. But he put you in a no win situation. That's totally about him, and not at all about you. If you tell yourself that and believe it, his blame will not affect you as stronglymuch.
YouI believe you are doing the right thing by protecting your mother. If he can't or won't understand that, that's his problem.
I have additional training and certification in mental illness and substance abuse and ran a clinic for same for almost three years. Also, I've lived with two people with NPD (one was my father) and have had up-close and personal, painful experiences with them. From a clinical viewpoint, they are fascinating people to observe and I have a special interest in NPD. PleasePlease feel free to DV and comment if this is off track.