My girlfriend is not being fair when it comes to my daughter?

My GF and I have been together for 8 years. She has her kids full time and I have my daughter 1 week out of two.

My daughter is 10 and her kids son 12 and daughter 14.

My gf has a big authority problem with her kids. They never listen to her and they do what they want most of the time. They do listen to me but most of the time I have to pressure them to do their chores.

My daughter does not like her stepmother. The fact that the SM is very lazy and is not listen to by her own kids does not make a good example.

Usually the weekend her kids leaves for their father my daughter is with their mother. So we get a free weekend alone. However in the last year most of the times her kids refuse to go see their father so we never get a weekend alone. My daughter always stays with her mother when it’s her week.

Now this week-end her kids are leaving but I have arranged to have my daughter with me. We always go camping but now my gf refuses to go because my daughter will be there. Even though I have spent time with her children time and time again she refuses to come now that we are alone. I’m not asking the gf to spend time with my daughter just to come. My gf brother has a camper and will be there and she spends her time there anyway.

What are you thoughts? Am I wrong?

What should I do to change her mind?