If I remember correctly, Abby's father had said that Jessica had something at a party with several guys at the same time and any one of them could be the father.
My guess: One of Abby's paternal grandparents died. These grandparents never bought into their son's thing with Jessica and felt bad for her. As a result, they disinherited their son-man and probably hired someone to track down Jessica and her child. He, in turn, found out that Frank was taking care of Jessica and the child. Glad that the mess their son made didn't ruin anyone's life, the grandparents left it up to Jessica's death. They may have continued to keep tabs on Frank and Abby after Frank married Shannon, possibly doing research on Shannon since they still felt responsible for their granddaughter, and then found out about Shannon and Jessica's past in the process. The private investigator hired then kept tabs on Shannon and found out about Shannon's affair and called Frank.
Abby's father, meanwhile, hopes that if he has contact with his daughter, he can then gain influence over the inheritance to some degree. Abby will probably tell him to go to hell.