It sounds shit for everyone, the dynamics are weird for you all and she is uncomfortable and lashing out. Talk of coming home early or punishing when she gets home seems counterproductive to me - you want to try and enjoy the rest of the holiday as far as possible, not reinforce the difficult relationship or carry on the battle longer than necessary.
I think I am in the minority but I would handle things very differently. My DDs are 15 and 16, definitely not entitled although they have their moments. Not step children, but in your case I think that just makes it more important that you find a working dynamic and get to know each other rather than fighting all the time.
Questions like the towel and the tap - just answer them. Yes she could have checked for herself but she's in a new place and kids ask questions like that all the time. Use humour if you can (but not mocking her).
'Where do I hang my towel'? Why don't you use the hook on back of bathroom door?
'How does this tap work'? Just like home, pull up and water comes out. Left for cold, Right for hot...
'Open this bottle for me' - definitely use humour. "Your wish is my command, DSD". Then hand her opened bottle and remind her to say please next time.
The ruder comments... actually seem to me that she wants to be included a bit more.
'TV is shit'.. Don't react to the language - either agree it was shit as pp suggested or say it was not bad actually but since everyone's ready now let's get going - then switch off TV and head out as planned.
'Drunken arses' - is rude, but don't take personally. Try a totally different approach at the time (then DH could discuss calmly another time if he thinks necessary).
I would have replied 'Haha, not sure we can stagger up the stairs. If you want to come back we could play some cards (or whatever), otherwise we'll be up soon'.
Maybe it is a good idea for your DH to spend some one on one time with her, you'll get a break and she'll not be the third wheel (not saying you're treating her like that, just that she may feel it). And lots of
for you!!
Good luck