Custody and visitation when neither party has legal custody

Hello, I am new to the site and I am presenting myself as a third party in an ongoing dispute. Basically, my girlfriend (Jill) has separated from her husband (Jack) of 5 years, with whom she was raising the daughter (Jane) of one of Jill’s brothers since birth. The little girl was born premature and addicted to crack cocaine and requires some medical attention which Jill has provided since birth. Jack is a construction worker and provides financial support but little else as he is illiterate and cannot read or write. He has provided minimal support in the day-to-day upbringing of the child but has gone to work and provided money to take of the regular expenses. Jane’s father, who has maintained sole legal custody of Jane, has shown no real interest in bringing her to his home (he is out of state) but he has gradually gotten his act together and is in a much better position now to take care of his daughter.
Since Jill decided to separate from Jack, he has become threatening and verbally abusive, to the point of requiring a temporary domestic violence protective order be issued against him. He was served with the order and vacated the premises that very night. In the follow-up hearing before the judge, an agreement was reached between the plaintiff and the defendants’ attorneys in which a “no contact” rule was applied to both parties and a stipulation was added that Jack would be allowed visitation to see Jane on Sundays when Jane was at her sitters’ home (not necessarily every Sunday!). Shortly after the agreement was signed off by both parties, Jack made statements to the sitter and other parties that he had no intention of following the terms of the agreement, that he was going to get his wife back, etc. Shortly after that, he made repeated calls to the sitter to make arrangements for his visits some of which he showed up later than planned, some the sitter had already made plans to be out-of-town for that weekend, in any event, there have been more misses than hits on the visitation plans. Jack has gotten in contact with his attorney and stated that we have deliberately blocked him from seeing Jane per the terms of the agreement and our position is that he has no legal claim to custody or visitation and that he will get to see Jane when all parties can agree to an appropriate date and time for him to see her.
I guess my question is this: What are the rights of a non-custodial adult who is not biologically connected to the minor child other than by association? If push comes to shove, Jane can be sent home to her father who is now willing to take her into his home and who has sole custodial rights to the child. Are we obliged to grant visitation to Jack only on his say so, even though we feel he is merely using that as a means to stay in contact with Jill in the hopes of getting her back? I hope to hear your opinions on this matter.

Your girlfriend should file a child custody claim. Even though she is not a biological parent, based on the facts presented, it seems she would have a valid claim for custody. Refer to the child custody statutes for more information.