omf, I don't mean to sound critical - I worded that badly.
But, she's 16. I really can't think of a reason why a 16 year old should be up at 2am. Teenagers do transmogrify into hideous people from one minute to the next - and, being tired is not going to help.
Am glad that you are getting closer to getting this sorted...but...she's now away to a friends? What?
She disrespects you, her dad, her sister. She lies, she steals, she leaves you to sort out her mess and is then a cheeky minx when you reprimand her about it...and now, she's out having fun at a friends?
Yes, I see that you are glad of a break...but, what is she going to learn from this scenario?
Lastly, just to sound critical - why are you allowing your 16 year old to be alone with a boy who is too drunk to know what he is doing? And, why are drunk young boys sleeping over on your sofa?
And, what are his parent's doing about this? Can't you, her dad and his parents put up a united front here?
Is it possible that you laying down the law is a new experience, and one that she doesn't like?
You want some advice? Get her back home. Take away everything that is important to her for a period of time longer than she'd comfortably bear. and do these things to punish her for the cheek and the lies that she's delivered to you.
Pick yourself up a pair of earplugs and a bottle of wine on the way home - and good luck.