No reason you should listen to me but here goes. I've read almost all your posts, not many of the others.
I really hope you feel you have had a chance to ventilate and enough useful support in amongst the everything else to help a bit.
You've got two really sensible ideas, go away for half term with your DC and look at having a separate home from DH for the time being. If you legally separate you can have separate homes with less of a financial penalty even if you hope and intend to reunite one day. You sound completely sensible enough to ignore any feeling of 'can't let SD win'.
Your DH might then be in a better position to ask for Social Services help with his troubled teen. I realise there might not be a lot of help on offer.
Looking in my crystal ball (eg what do I really know? - nothing) it might be the best way to prevent intolerable stress from really damaging your relationship with DH long term. If you're not constantly dealing with the shit you might be able to give him better support and he might feel less conflicted if he's bravely on the frontline while younger DC are safe elsewhere.
Last two pennorth: its good to vent but I think, in the long run, it might not be good for your equanimity to hate SD. If you can you need to detach. I say this from a place of empathy having had a similar issue, but with an adult, this year. I regarded them as family, bent over backwards, no good deed went unpunished.
To those criticizing OP: 15yo boys sometimes physically bully mothers/stepmother and this should be seen as domestic abuse. It is not ok. Domestic abuse is not just physical violence. We don't know what line has been crossed here but there's no reason to assume a 15yo girl is incapable of abusive behaviour. Threatening to or actually carrying out mendacious legal complaints and false allegations to social services about child abuse by a parent towards their DC is serious stuff.