Answer: I think you can maintain the same transportation arrangements at least until the end of the quarter. While the school can’t force a parent to participate in the after-school program as a condition of transportation to the school of origin, the school does have some flexibility in providing transportation, as long as it is safe and appropriate. In this case, the boys will continue to be safe staying at school until after the tutoring program. The school can tell the parent that the transportation will continue to run after the program. As you know, you are “required to ensure that transportation is provided” to and from the school of origin.
The only caveat would be if there is some safety reason, or other reason related to homelessness, that the parent wants the boys home earlier. For example: if they are staying in an unsafe area, and as it is getting darker earlier, the boys would have a dangerous walk from the bus stop to their home. Or, for example, they are staying at a shelter that requires the whole family to be at the shelter by a particular time to access the shelter. If there is a safety or related issue, that could present a barrier to enrollment and retention (and potentially put the school district at risk for liability). In that case, the district would need to get them home immediately after school.