Hugs Lu, you are doing a fantastic job. Stick to your guns.
DD1 moved into my dad's house last year for 8 months because we were "unreasonable and controlling" Sadly my dad gave her too much freedom but he also didn't wash for her, cook for her, make her lunch etc and she moved back with us last November after we had an open and frank discussion about how much we loved her but had rules for a reason.
Its not always been perfect but I think she is older and wiser from it and appreciates living in a family where she gets fed and cared for. The big thing was recently her cat was badly injured and had huge vet bills- DH hates the cat but he called his sister to borrow the money and now we are all going without tonnes of things (including food LOL) to pay her back. This made Jess really see what families do for one another, she has been working extra hours at Maccas to help pay for things and really appreciates what it means to be a family.
I am finding that explaining to her why I am saying no helps a bit but really its an irrational age, 16, sadly I think you just have to wait it out.