No they don’t.
Parents carry financial responsibility until 18 but courts schools and law enforcement cater to the child from about 12 on. Abortions, where to live, whether a child comes home or stays out all night, who they see, media and internet, is all non enforceable by parents.
The law will side with the child often.
My advice. Cut the kid loose. Minimal financial support or encourage him to legally emancipate. If I were to have children today I would do it on a large farm with no electronics, homeschooled.
So that leaves two options. One, move with the family to a very rural and isolated locale (no internet) and do that “commando parenting” espoused by Dr. Phil. Or, two, as you said, grant the little horror the emancipation she so desires and not one cent. She’ll be turning tricks and doing drugs in short order. Long gone before 25 or 30 unless she turns to the Lord.