When I read the Gold Rush complainant's letter, I thought it might be my sister. A couple of the details are off, but the general circumstance is the same, and my sister's reaction nearly identical.
So, yeah, my father ditched my family for another woman. But, I'd never had a particularly close relationship with my father (or anyone in my family, really), so I had the ability to take it philosophically. My sister, on the other hand, had been daddy's girl, and when she wasn't anymore she kinda went nuts.
Ironically, my step-mother was killed (very) recently in a hiking accident. Since then my father has been reaching out to us, and he began the process with an apology.
I told him it was okay, that I didn't really feel there was a lot to forgive. He really loved the Other Woman, and as far as I could tell, she treated him right. My own mother and my father never got along well. My step-mother clearly hated my guts (trust me on this one), but she and my father got along swimmingly. I figured that's a pretty inarguable good. Sure, it meant I didn't get birthday presents, but I have a loving wife and good friends who made up the difference. It was better he be alive and happy without me than alive and unhappy with me. And it was certainly better than him being actually dead. That'd suck.
While it'd be pretty easy to identify my late step-mother as a gold-digger, because marrying my dad was a social step up for her, she stuck with him for the long haul. That's not gold-digging. Gold-digging is marrying a guy, spending his money, then divorcing him so you're free to do it again. That's what one of my aunts did. I didn't like her, and I thought their love was creepy and weird, but it was love and I know better than to try and pick a fight with that.
Anyway, my advice on the matter is let it go. Maybe send a birthday card once a year. Don't send gifts, or expect gifts. Don't invest a lot of emotion. Don't write dramatic letters of protest. You're just being polite, like you would with an old drinking buddy who shipped off the opposite coast for a job. Metaphorically, you want to leave the door unlocked, but you don't need to let the chill in.
Being an adult means making the best of bad business, and more importantly having the humility to recognise that you can't rule over the emotions of another person.