Yes.
They have a legal obligation to abide by whatever the officially designated next of kin (or delegate) tells them. That have to do it that way, because otherwise they would have complete chaos. It’s not their job to decide who gets to make the decisions.
I know you mean well, but putting it in writing doesn’t amount to anything. People think it does, but it does not.
What is important is to make sure that you delegate someone (whom you expect to survive your own death) whom you can trust to carry out your wishes and then leave that trusted person written instructions.
Finally, with regard to contacting a priest:
Try the three diocese of Arlington, Washington, and Baltimore (in that order). Contact the chanceries and ask for an available priest or deacon, and don’t forget to ask them to suggest a retiree.
Try calling the Theology department at Catholic University and ask for a priest.
Try Theological College (don’t forget to ask about a deacon).
Call the various and sundry religious order houses around Catholic University.
It might take you some time on the phone, but surely one of them will have a priest or deacon (don’t forget to ask about a deacon! Arlington Diocese alone has 90 of them) who can spare a few hours to assist at a burial.
