D.B.
I'm a stepmother. I know how hard this is - and I know how hard teens are in general.
Your boyfriend's daughter has been through a lot. A teen girl needs her mother and she's feeling the loss no matter how messed up the mother is. You are making a valiant effort to step in, but you are not her parent and you are not even her legal stepmother (which she knows) so you have no authority. She may feel a little abandoned (or a lot) by her father, and she may be trying to push you away to bring him back home. If you weren't, there, he'd have to come home, right? That may be how she's thinking. Or, she's proving that she's basically "unloved" and "unwanted" by having neither her father nor her mother involved, so she goes for the aunt, only partly because there are no chores etc.
He's confused.- he's to be her father without being there. He's trying to make plans from afar but he's not clear enough on the schedule or the impact. And he's not there to reinforce anything. So you become the bad guy. You've been doing this for 2 years, it's not working, but you're still doing it?
If she's lying and has no supervision, he's doing her no favors, and it's going to get much worse when she's tempted by cars, drugs, sex and alcohol. Bottom line - it's his daughter and he has to decide. If he picks the aunt, then he picks the aunt. But he has to pick. Maybe he needs a job that doesn't take him on the road all week. That would be my recommendation frankly. She has a hands-off mother and a clueless, distant father. She's acting out by lying and he's falling for it because it's easier than being strong.
Parenting is hard. I'm sorry his heart's not in it. And I'm sorry he doesn't care enough about you to work on a solution that respects you.