I think that it is not helpful to see the latest developments as being so dramatic, so catastrophic, so final or so black or white as you describe. I think that tough love or cutting him off is a very dangerous approach.
All of that just plays to the invented delusional narrative of the unstable histrionic teenage girl and her enabling mother. Don’t give it the credibility or power of triggering you emotionally.
They have been rattling your cage, provoking you and exasperating you until you are done.
Step back and step up.
Step back from your initial triggered emotional reactions which inadvertently contribute directly to the drama and step up into a professionally informed emotionally strategic approach.
Your DS seems to be absorbing, mimicking and mirroring and then transferring her BDP traits - the histrionics, conflict, blaming, pushing you to abandonment - directly on to you rather than it rattling back between the two of them which is where it needs to stay to erode the relationship - but somehow you have become a their “target of blame” which is a central and mutual energy in this highly strung RS system.
Take yourself and this energy out of their RS - but DO NOT take yourself out of your DS life - instead read the book mentioned earlier and employ the detached love tactics which involves you dialling down the emotional heat - stepping out of their drama triangle and instead being cool but firm and ensuring boundaries are CALMLY and consistently enforced with usual actions and consequences.
You and your family need to be the contrast to his life with her not another version of intense emotion, scrutiny and over reaction that has him ricocheting hurt, confused and distracted between you both.
So reframe it all - you are not chasing him out of there but you are instead attracting him back with balance, peace, calm, mental space, freedom and fun.
You personally should NOT front these activities, but be responsible for planning them behind the scenes - it has to be friends, family, siblings etc who are the centre of the invites - plan simple fun things that you know he would like to join in where he isn’t the centre of attention. You are trying to bring him back to experiences of balance, light hearted fun stuff.
And he is just away for a few days - imagine like a school trip - there is absolutely no version that this is a permanent pattern or move and this will be discussed and negotiated with him in time after the emotion has died down when things are calmer. That is where the calm firm expectations of him come in.
It’s like a long game of chess. Take the emotion out of it and play it strategically with skill.
Get professional support and believe that by the end of the year all will be fine.