I am soo not a morning person either. I am dressed by the time my first kids arrive, but I am almost always wearing sweats with my hair in a pony and I never wear makeup. That is pretty much my everyday attire, daycare or not (why dress up if I'm always at home?). One or both of my kids has either just woken up (or is still sleeping) and is still in their pjs, but my parents don't mind.
I think it is a given that a parent will be tired in the morning, especially with young kids.
Next time she says something I would just outright ask her what her issue is, and just tell her that if she doesn't trust you to look after her child, then maybe she needs to find alternate care.
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