Generally it's accepted that the parents have the right to make decisions regarding their children.
If the parents are divorced, how many pieces do you want to split this child into? If each parent has the child EOW, then if you get one weekend a month, you're taking half the family time that child has with one parent. Even if you get one day a month, that's 25% of the child's family time with one parent. Not to mention, the question becomes, what caused the estrangement in the first place? What if the parents want or need to move out of the area? Are you going to refuse to allow them to do that? What if the parents can't find work?
Not to mention that you have to remember that court isn't cheap. The parents will need to hire an attorney. That could potentially be food out of your GC's mouth, or opportunities they can't have, because you're taking their parents to court.
You need to consider whether an extended court fight is really in the best interests of your GC.