Since only you know your daughter and the particular circuмstances more than any of us, I wish to share some Catholic principles which I have confidence you and your wife have the prudence and charity to properly implement. I am deeply interested in psychology and can also offer some ideas that may or may not apply to your daughter.
Your family is in my prayers.
Sin has always been regarded by the Church as the only true evil. We must be willing to sacrifice everything temporal to avoid sin, and the proximate occasions of sin. This also applies to those under our care, in that we must be willing to punish in a way that results in temporal losses, if that is the only way to effect a cure of the evil.
What is the greater evil: the harm done to your other children along with your daughter's obstinacy, or her being forced to face reality by a severe punishment?
Extreme measures seem to be the only option at this point, if she is truly doing this through malice, rather than some other motive. Women often continue in their wicked behaviour despite threats, because they do not believe the threats were made seriously. Perhaps if you begin packing her bags, she would come to her senses. Alternatively, maybe you could make a campfire and burn all of her immodest clothing in front of her. The key is, to do something that would make a deep impression, deep enough to bring her back to the Faith (that is, again, if this would truly be the only way to bring her amendment. Using reason and gentleness is always to be preferred, if circuмstances permit). As the father, you have authority from God to do everything you can to ensure His holy law is observed.
On the other hand, women are sometimes rebellious, particularly towards men in their lives who have authority, because of a hidden resentment or feeling of betrayal. In the case where a father was unjust at some point in the child's life, this can make the daughter lose all respect for the father; it could be something from many years ago that was never resolved. Perhaps you can request that she have a one on one with you, present yourself humbly and meekly, and make her feel safe with your words and actions, to the point where she feels she can open up to you, to have a heart to heart. Your wife could also do the same with her, and this would give her that sense of safety, that her parents are united in desiring her welfare. She must understand and be convinced, that at the root of your orders, is a desire for her welfare. In my experience, children with this type of rebellion and anger as I have described, deep down, do not feel loved by their parents, and are more moved to amend themselves through knowledge of this love, than through fear.