My guess:
Abby's biological father and his wife can't have kids for whatever reason, maybe karma degraded his dick to a limp noodle after what got pulled with Jess. Then he remembers, "Hey, almost 20 years ago I got my then-girlfriend pregnant. Maybe I should check out if there's still a need for a father. And since my then-flame passed away years ago, maybe I should bring my wife and sweeten the deal with a stepmom in the super deal."
But yes, a possible inheritance that remains forfeited to him until he puts things of his past in order I think is well within the realm of possibility. Who knows maybe he needs an organ or bone marrow donation and Abby is the only living relative he has.
But seriously, this guy is plenty late and I can't imagine someone like this deserving a redemption arc. Again, I see it differently with the mother of the woman who ran over Jess (although I can certainly understand Frank's anger). I would have liked her to have contacted me at least a few months before she died and talked to the two of them. I have the feeling that she saw Jess as a kind of daughter that she would have liked to have as a biological daughter and Abby as the desired granddaughter that was never granted to her. But well, the plot doesn't give that option and I think that's quite ok, she supported Frank and Abby as best she could and that's all you can ask, I think.
That Shannon contacted Abby's biological father, however, I doubt: her bio indicates that she thinks Frank is Abby's biological father, and the resulting resentment that he had a child with Jess ultimately caused (or accelerated) the breakdown of Frank and Shannon's marriage. After all, she herself was quite distant at the time Jessica and Frank got together. By that time, Becca was already in the world, and Shannon may have been pregnant with Lilli at that point. What I can imagine, however, would be the following scenario:
Shannon wants to confront Frank -> This happens to be the day Frank and Abby meet with Abby's father -> She realizes that Frank is not Abby's father -> She talks to Abby's father in private and the two become allies.
It would be Shannon's goal to separate Frank and Abby, especially in the face of grooming and loco parents, which could cause some complications for Frank.