Answer: Let’s talk through the non McKinney-Vento legalities first, for context. These caregivers have no legal rights over the child unless the parents or a court gives them rights. The parent(s) could sign a simple power of attorney that gives the caregiver(s) the right to make medical, educational and other decisions. That would be legally valid and does not need court involvement. There also could be court involvement and a guardianship or custody order, but that is less likely, due to the cost and time involved, if nothing else.
So in this situation, where it sounds like there is nothing giving the caregivers any rights (neither power of attorney nor court order), then McKinney-Vento is clear and rules the day. The student is an unaccompanied youth, and therefore the school must prioritize her wishes. (ESSA now requires that the liaison “assists in placement or enrollment decisions…, gives priority to the views of such unaccompanied youth, and provides notice to such youth of the right to appeal.”) So the liaison must assist in the decision and prioritize the student’s wishes. If he and the student are in agreement about school of origin, then that is where the student should attend. The caregivers have no legal say in the decision and no right to access the appeal process, because the youth can access the appeal process on her own.
If the caregivers get a power of attorney, then things change. While the liaison still must assist in the decision and prioritize the views of the youth, the caregivers have legal rights. The caregiver should be able to access to the dispute process. If they get an actual court order making them legal guardians, then the student technically is no longer an “unaccompanied youth”, and so in that case I think you have to treat the caregivers like parents.