Dear ((((((((((((((((Movinon)))))))))))))))))))):
Think about it. She's a little girl and her mommy is super-stressed (because mommy is dealing with the king of jerks but that little girl doesn't know or understand that. All she knows is she wants her daddy. Probably not even because he's any kind of daddy to her but because kids want a mommy and a daddy period!).
And mommy is busy, working hard, trying to cope and keep everything together, struggling with so much......financially, emotionally, physically (are you tired physically, Movinon?). And she's a little girl who wants to have fun.
Ofcourse, it seeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeems like more fun at daddy's house. He doesn't have to deal with her tardiness. She can take her time and he doesn't mind because he doesn't have to deal with real life and obligations and time schedules and getting anywhere on time. She can take all the time she wants at daddy's house and this is just fine.
And the girlfriend? What would she require of your little girl? Nothing, probably. The gf is new and if she has any brains whatsoever she isn't going to stampede in and start giving orders. So .......she's just like a new play mate for your little girl. Someone new and fun to be around. The gf doesn't have to deal with real life and teaching anything or guiding or encouraging or disciplining or the physical work of meals and shopping and laundry and fevers or school or grumpy moods or fussiness or tardiness or anything else real. The gf can let your daughter do annnnnnnything because it's no skin off her nose. And it's only for a short visit.
First.........your feelings are valid (people are going to get sick of seeing me write that but I just can't help it!

). If there is a single mother alive, especially one who has to deal with a jerk like your ex, who doesn't get where you are.....how you're feeling and the frustration and the anger and the disappointment and the exhaustion etc, etc, etc,.........well...............I just don't think we will find one who doesn't. Anyone who has been a single mom knows darn close what it's like for you and most have felt similar stuff.
You have a lot on your plate and it's not easy.
So my (as other's have called it.......unsolicited advice) is...........
1. Please do something for yourself.........find a counsellor/pastor/go to a women's shelter and find someone to talk with about your feelings because right now..........it can't hurt. It will only help you to have another person on your side, who will listen and help you through your feelings.
2. Stop .........reacting to your daughter. Just stop. Tell yourself you must and do it.
Instead.......ask........."How does that make you feel?" and listen. Talk. At six.......it's hard to put feelings into words eh?
3. Believe that she is a sweet little girl who only wants a mommy and a daddy who love her and that she has a lot on her little plate too. She has to adapt to all of this change (and to the constant changing going on at his house). She has to feel and be sensing some of your feelings.......which she may be absorbing and not dealing with well herself. Believe that she loves you and understand that she needs your constant, reliable, everlasting stabile love. That's what she longs for (but ofcourse she is too small to know it). That you will not divorce her. That you will love her no matter how she behaves. That you will be there for her and won't disappear and not visit (like her daddy did).
4. Try to make life at your house a bit more fun. Play a board game. Bake some cookies. Do a craft. Go for a walk, swim, bike ride. Anything to be with eachother and enjoying time together. Focus on her, at those times, and let her know how much you enjoy her, like her, want to be with her.
I'm so sorry for how hard all of this is Movinon. It's a lot of work and you have to use your last bit of energy to stay close to your child. As she matures, she will indeed know the difference between those who actually care about her (you) and those who use her for whatever selfish needs they have (her dad) and when that happens......when that awareness comes to her.......she will need you more than ever.
(((((((((((((((Movinon))))))))))))))))
Sela