Yes, it does seem that the parents want you to do the dirty deed. It won't be
easy if she has slept in Mom's room for 7 years and should go "cold turkey"
now.
Perhaps you can strike a deal with the girl. Tell her that you'll stay and read
her a story if she promises to be good and go to sleep afterwards. You also
have to tell her what happens if she doesn't comply - no bedtime story and
lights off immediately.
It's a rotten thing to do for the mother to let you do the weening off, it really
should be her job, but I think you like the girl and have compassion, so it's
better to help her than leave her traumatized and scared in her room alone.