Imagine the scenario (all hypotetical, I am happily married most days): my husband walks out on me and our baby son and has no interest in having access or contact. Five years down the line, I end up in a stable, loving lesbian partnership and my new lesbian partner is my son's best friend, enormous support and generally a fantastic replacement for a lousy father who walked away. Another five years on, I die and my loving, caring lesbian partner has to hand over my son to either un-interested father or the state? How is this fair and in better interest of my son than him being adopted and cared for by my lesbian partner?
The situation would be no different if your second relationship was a heterosexual one. So, why should a lesbian partner have more rights than a heterosexual partner?