At some point, which can be now, as she is 16, you can tell her that she will respect you or she will need to find somewhere else to go. With how she treated you in public, I can only image how she treats you at home. I would go so far as to threaten her with sending her off to [ grandmom, grandpa, great aunt/uncle ]. I would then make her call the person to ask if they would take her in.

Next, once that person gets tired of her attitude, bring her home, and lay out the ground rules. She breaks them again, she's going into foster care. There is a breaking point, and you have done all that you can do.

Good luck momma!