Your last sentence/question may be one to pose to both parents.
I, too, have a dysfunctional family.
Instead of helping one another, they get caught up in wounds and in retribution -- and it's all crazy-making. Instead of "stepping up," people want to nurse old wounds and will not help anyone truly in serious need. They are too caught up in themselves.
My family used to try to put me in the middle; however, they cannot force me into the middle. If I don't take the bait, I am not in the middle of anything.
No amount of conversing changed the patterns they are locked into. it looks like they love to despise one another, love the drama, etc.
I had to let go and totally do my own thing, find my own support elsewhere, etc.
It can be difficult to "let go" of your role with your family; yet, your sanity may depend upon allowing the to hash out their own stuff without getting involved.
Will your parents sort out their communication with each other (eventually) if you refuse to play that role?
What happens if you let go of this role of being in the middle?
Take good care of yourself.

WC