In 1985, right after the events of Peter, she is seen comforting Walternate over the loss of their son. ("Subject 13")
Later on in Season 3, Walternate is seen with his mistress implying that they are no longer together or that he is cheating on her. ("Immortality")
Season Four (Alternate Timeline)Edit
In the alternate timeline, Peter was still taken but he died when Walter took him back to the other side so she never got to have a reunion with him.
When Peter enters her house, wanting to find Walternate as he thinks he can help him get back, Elizabeth instantly recognizes him. She protects him and takes him to see Walternate after this. ("Back to Where You've Never Been") Later on, she crosses over to talk to Walter and convince him to help Peter get back to his timeline. ("Enemy of My Enemy")