I think you nailed it when you said she needs a morning nap - she sounds exhausted.

It is also probably in an attempt to blame things on teething, etc. that the parents have bought into the want for attention and now it is a need not just a want because she has lost the ability to be self-sufficient - ie the parents took away her ability to cope. Does she go to bed for the parents or do they rock her to sleep with a bottle, etc. Do they let her cry when she wakes up or do they go to her right away. My guess is they are back to attending to her every whim and now she thinks she should be king of the castle at your house too.

I have a real thing for kids that need a morning nap In most cases it isn't the child's fault it is the parent's fault for not getting the child into bed in time to have a full quota of sleep. I would be rethinking your schedule and what prevents you from giving her a nap and make changes. If you can't then she needs to go to a home where morning naps are allowed.

Parent needs to be on board if you are going to make any progress since child is not with you long enough. What does child do on the days she is with parents and how do they deal with her - they don't likely see the problem because they don't experience it - they are too busy creating it.