We are in the middle of an argument about my 7 yo stepdaughter right now help.?

Stepdaughter background well behaved, loving. Her mom extremely permissive would not ever raise her voice at her and very dedicated to her. Me, I have an 11 yo boy well behaved. Him, extremely good father and bf. So our relationship has been suffering for a while because I am freaked out to say the least. His daughter has lied in various occasions for various reasons, not to get in trouble (normal), has made up huger elaborate stories not about me or my son yet. Thats the question, how long before she starts making up stories about me or my son or even her dad to get the attention and continue the manipulation of her mother who doesnt know any better. I can specify about her lies if u all need to know. Why are we argueing today is because she told her mother her arm hurt and that i had put medicine on her yesterday as soon as we dropped her off. There was no pain in her arm, n def no medicine. We did spend a lot of time time yesterday talking not lying throughout the day and thats the first thing she does as soon as she sees her mom last night. I told him, to go talk to both of them today and tell his daughter she will not come with us (FUN,POOL) because she lied about us yesterday and send her a direct stern message. He disagrees because he says he should be there for his daughter no matter what. He wants to talk to her about lying (did so yesterday already and many other times) I am freaking out because i do not want to lose him for any other lie she could come up with that could get us in trouble with the law. We currently do not let the kids play together, or his daughter away from our sight for a SECOND. Because of the lies. I need help.