I don't think your proposed letter will work. She is shoving her in the door and running so you can't check and refuse care because mom will be gone before you check.
I would write up a letter of probation. If the child arrives in panties only again care will be terminated as of the next day. I would send this letter home, email it and text the content. Make it CLEAR that this begins tomorrow.
They clearly think they can manipulate you until you cave...make it clear they are on their last chance and the consequence of dropping in panties and running is they have nowhere to go the next day.
This is no longer about potty training this is them trying to win the situation and you do NOT benefit if they win this one as they will feel they control you.
:-(