Answer: There is no problem with this, as long as the transportation provided by the shelter is cost-effective. McKinney-Vento allows the LEA to provide or arrange transportation, thereby giving the LEA some discretion to choose the method of transportation, as long as it is appropriate. In this case, if the shelter has the capacity to provide appropriate and cost-effective transportation, the use of Title I funds would be allowable in the same way as it would be to reimburse a parent or provide a school bus. As many communities are struggling with school bus and driver shortages, working with the shelter in this way might make excellent sense.
The only concern here would be if the shelter transportation stigmatizes the children. For example, we have heard horrible stories about children being driven to school in vans with the name of a shelter in giant letters on the side. This can lead to severe stigma and discrimination. It is important to keep that in mind and ensure the transportation avoids stigma.