Child Abandonment by Mother and Custody

My question involves a child custody case from the State of: pennsylvania. My fiancé went to the gym one day when he came home the mother of their daughter left the baby in her crib unsupervised, he’s not sure how long the baby was left alone, couldn’t be more than two hours. She never came back, this happened when the baby was about 6 months, she’s 3 now, the mother just started to contact him demanding he takes the daughter to Boston where she now lives so that she can see her. She also has 3 other children by three other fathers besides the one with my fiancé and she doesn’t have any of them. When she left he just figured that she obviously didn’t care about her and wouldn’t be bothering them in the future, he couldn’t grasp one doing that and then wanting to see them out of the blue especially over a year later. He does not have full custody but obviously doesn’t want his daughter around her because he thinks it’s not healthy to be in and out of her life, she could do it again and this time being that she’s three she would remember, right now she doesn’t remember her, she sees me as the mother figure, clearly I am not but she’s happy and so are we. He doesn’t know what to do in many ways, same with me.. a bit of me feels guilty keeping a child from their birth mother and then there’s always the fact that she can get hurt if she just stops visiting her one day. If anyone has opinions on the “right” thing to do please give me some advice and also how to go about getting full custody.

Child Abandonment by Mother and Custody