Divorced couple's unconventional parenting arrangement causes conflict with new boyfriend

A divorced couple's decision to buy two semi-detached houses with a door connecting them for the sake of co-parenting their daughter has caused friction with the mother's new boyfriend. The boyfriend, who knew about the arrangement when they started dating, has become uncomfortable with the close proximity of the ex-husband and has asked the mother to move in with him instead. However, the mother has refused, citing their daughter's need for stability and the success of their unique co-parenting arrangement. The disagreement has raised questions about the boyfriend's role in the family and whether or not he has a right to be called the daughter's father. Readers are left wondering if the mother is being unreasonable, or if the boyfriend is stepping out of bounds.