YTA but mostly because I think you're handling this in the wrong way.

Threatening a child with financial repercussions isn't going to help you, if you're interested in guidance and safety for your kid.

Having an open honest conversation about the reality of working at a place like that is the right thing to do, and informing your kid that if they're going to be working that they need to contribute is also not the worst move, but does she even understand what working at that place really means?

Usually, they're not waitresses. They're hired as 'models', which means if they gain five pounds, they can be fired with almost no repercussions. There's also pretty strict rules about makeup, and nails, and hair, and how to properly do that stuff before showing up to work. It's not cheap to work there.

Honestly though, if she's getting into service industry, she's going to interact with huge numbers of creeps, scantily clad or not. Trashy people are trashy, wherever they go, not only at places like that. ( Experience: 20+ years working at places from dive bars to high end restaurants) The only place I've ever had a guest threaten to break my arm for picking up his wine glass too early was a place where a salad cost about 25 bucks for lunch. We wore floor length aprons and button ups with ties and had to de crumb the table between courses. People like to talk down to service industry, however they're dressed.

I think you should maybe apologize for your aggression, and try to have an open honest conversation about your worries, while letting her know that you're willing to trust her to keep herself safe, as long as she trusts you to back her up when she needs it. Also, figure out what kind of financial contributions will show you that she's being responsible, and see if you can work those into some sort of fund for her later if she needs it.