Edwina

Edwina is a woman whom Abe Simpson had a relationship with while he was stationed in England during. She is the mother of Abbey.

History
Abe met Edwina during the war, and led her to believe he was being shipped out the next day—evidently, in order to make the relationship progress faster, in physical terms. To Abe's surprise, he really was shipped out the next day for. Unbeknownst to either Abe or Edwina, he had gotten her pregnant. Nine months later, Abbey was born.

Abe and Edwina lost touch after D-Day, and Abe had no idea Abbey even existed until 59 years later when he re-encountered Edwina during a family vacation in London. Homer, Marge and the kids vacationed in England and Abe tagged along in order to search for Edwina. He had no luck finding her, but she tracked him down and met him in the airport just as the family was about to fly back home. Edwina then introduced Abbey to Abe and the rest of the Simpson family, saying that she was fifty-eight. Abe laughed and started to tell Abbey that fifty-nine years ago he had known her mother really well, but then it dawned on Abe who Abbey was. With that realization, Abe fled for the plane.

Behind the Laughter
Although not explicitly stated, it is strongly implied that Abbey is Abe's biological daughter from his brief relationship with Edwina.