I have a daughter myself that can be difficult.
A lot can be understood from theology. See what she is saying about the WELS and how she doesn't want you to say anything and so on. She's reacting in one of the normal ways to law. She's lashing back, not willing to obey.
A real thing to find out is why? Is it that she never really heard and believed the gospel?
It is so popular with some to cut off children. She already knows you don't approve, you don't really need to say anything about that. Let her know though how you really do love her, how hard it is for you to see her go, especially so far away and so on. Really open up to her that while it might seem to her that you are some dried up harsh lawgiver, the basic thing is you are trying to protect her, that you love her and you don't want to see her hurt. Speak of your faith, how it supports you and guides you. Somehow she doesn't seem to have gotten that. Yes, you've given rules and such for her to live by, but they were to protect her until she became capable of making decisions herself. Much like the law was given to us to be a trusted schoolmaster until we received the gospel.
Ask her if church is a wonderful place where she gets to go freely, or is church to her a burden, something she must do or at least is expected to do. Somehow I don't think she sees it as a gift.
Try and get her to open up. Is she afraid of being alone? Is it that she feels she must give herself to some man without being married in order to get a guy?
Explain how sex is a dangerous thing. Even in marriage sex is dangerous. You share diseases, history, children, a lot through sex. You worry because you are her father, and you don't want to see her hurt, that if she isn't married, it's easier for her to help her guy get established and then, when he is established he can swap her for that young something looking for a man with money. Without marriage she doesn't have much protection.
Let her know that whatever happens she is welcome. You aren't going to support things that dishonor God because you can't. But God made her your daughter and you her father and that isn't going to change.
She is an adult legally and she can make her own decisions even if you don't agree with them. You hope that she doesn't make decisions out of some sort of rebellion or spite. Hopefully she is enough of an adult to at least do things because she has thought them through, considered the consequences and is willing to accept them.
That will give her lots to think about.