That's a lot of chopping and changing for her. She's barely settled back home before she has to up sticks and head off again. Try to provide lots of structure and routines for her at your house. If you have a chance to spend time with her doing some cooking or baking or teaching her to knit, she will feel closer to you.
There's also a possibility that her dad may be overcompensating for his absence by letting her get away with things while she's at his house, which might be unsettling for her. It's hard to be the one who keeps a child's feet on the ground, with reasonable discipline, rules, and consequences, but better for everyone in the long run if you persist. Some of her behaviour (especially if it's rudeness, talking back, shouty attitude) may be down to blowing off steam and inability to express her real feelings.
She may be taking out her feelings about the separation on you (instead of sitting down and talking about them) because you're the one she feels most comfortable with. Have you talked with her about her feelings? If she hasn't been used to naming feelings up to now, this is the time to start. You can model it yourself by saying, for example 'When I lost the car keys I felt XXX'. or 'When the dog next door runs up and barks suddenly behind the fence, I feel XXX'. If she's giving everyone a hard time with hostile behaviour or cheekiness, take her aside to do something quietly like drawing or listening to music with earphones.
6 yo girls can be terribly stroppy even without a divorce thrown in. Don't let her get away with anything you really don't like out of guilt about separating from her father. I would try to see if she could have a less chopped up weekly schedule for visits though. It will get complicated if the current routine is maintained through her school years.