This answer does a good job of explaining how to focus the conversation (and your thinking) when talking with your father. I'll add something I saw in my extended family (in the midwestern US, involving the first and second generations post-immigration from Italy, for what that's worth).
One family member who was already a little erratic got upset about something, we never found out what, and cut off several family members (siblings and their children). The latter group thought this was a fine idea, especially after the former filed a frivolous lawsuit against the latter. Time passed. Eventually, one family member (one of those cousins) reconciled with the person and then tried to get others to get back in touch.
To which several of the others responded: we aren't the ones who broke off contact; if she now wants a relationship, it's on her to make amends. The message to the cousin -- whether it ever made it to the family member is unknown -- was that damage was done and she was going to have to at least apologize for it if fences were going to be mended. It can be difficult to apologize and admit you were wrong, especially after a lot of time has passed; it can be even more difficult for a third party to convince someone to do that.
This seems similar to your situation. You didn't break off contact; your mother did. If your mother wants to reconcile, you can tell your father, then she needs to act. Further, because of what happened in the past (remember, it's about deeds not the person), you're very uncomfortable being that vulnerable, but you're willing to give it a try if she understands and apologizes for what she did (and, if applicable, fixes some of the damage she did). Say all this with love and caring -- you're sad that this has come between you and your parents, you love your father and regret the bind he's in, you wish things could be different -- and it's not your move.
This moves the situation from "your father tries to persuade you" to "your father needs to get your mother to do something". He might or might not be willing to pursue that, and if he does he might or might not succeed, but the chances seem good that you'll be able to continue avoiding her without being the "bad guy" in your father's eyes.
All that said: if he does pursue it and if she does apologize, ask your forgiveness, and ask for another chance, at that point you really need to be willing to try if you want to preserve your relationship with your father. Either things will actually be better (score!) or they won't and you can then say "sorry, this isn't working" and exit.