Woodsy, excellent advice! I agree with you, in this child's situation it's the inconsistency at home.
I have asked all my parents to be here before 930 so we can start our day. Today she wasn't here and I texted asking when they would be. I got no answer. We continued on with our day and at 1045 the mom finally got back to me and said that her phone hasn't been going off (she uses it as an alarm) so I am assuming they have been sleeping in the past few days. She said she would be here by lunch. She knows we eat at 1145. She got here at 1215 as we were getting ready for nap and I told her that I would like her daughter be here at 930 whether she has slept the night before or not so that she can play all morning and be tired for nap time and then hopefully go to bed better for her. Mom has said she has been keeping her home to sleep because she didn't sleep at night and didn't want to bring her here cranky.
I put her daughter in her playpen for nap even though she likely wasn't tired. She cried for half an hour to 45 minutes and is now sleeping. I will just keep her to our routine here and hopefully mom gets her back on track at home.