I think letting a child back into the house full time with other siblings that she has basically rejected, whether step or not, for several years, is a toxic dynamic for your kids, let alone you.
Your children are not stupid and can see what has happened. They can see that their mother was accused of emotional abuse, and your SD insist that he sees her alone. They will know she dislikes you and dislikes them. If it happened over a few weeks, things could be forgiven and a decent harmony restored. Step kids do get stroppy and resentful. However running from one parent to the another for several months is a very toxic dynamic and one the parents should not have let happen.
This is ultimately her parents doing, he Mum and her Dad. Her Mum possibly revelled in it a bit, and your DH appeased her rather than standing firm. If he believed you had emotionally abused her he should not have stayed with you. If he didn’t believe it, he should have stood firm with his SD and say some things cross a line, that he loves her, but that he coudn’t just have contact outside the house.
That said, you would have thought that decent parents could probably just see a girl perhaps feeling ‘on her own’ and acting out, and just needing love from her Dad and maybe more attention.
I was in a similar position a while ago. I had a SD live with me for several years full-time, it was OK at first but really only if I was meek as a mouse. SD became more and more resentful and pretty mean to my children, which became exhausting as I had to intervene every time to make sure it didn’t turn into bullying of my kids who were younger. Having said that, there were no blazing arguments, just an ‘atmosphere’ from her to me and my kids. She ended up completely ignoring me and my children for many weeks and then one day I asked her to please stop. I said I’d had enough for being ignored and the least she could do was to acknowledge the other children respectfully. She reacted very badly, had a huge strop, and said she couldn’t live with me anymore and she was going to her Mums.
She totally ignored me all the time and refused to come to the house despite me asking quite a few times for her to come for dinner. DH of course took her out for meals, her Mum loved it and loads of horrible mean gossip went around the family, and still gets trotted out now as ‘fact’.
So when in 6 months time, apparently she wanted to move back in, I said NO. DH was really flattered that she wanted back. The reality was her Mum had got fed up of her, and didn’t her living there anymore. SD didn’t particularly want to come back but felt that if she did, I’d have been ‘silenced’ to never dare ask her to be civil again.
At that point, like you OP, I was quite prepared to split up from DH. SD was also 19 years old by then. I had my family to protect and my own mental wellbeing. It really had come to that. I was deeply sad that she had nothing but resentment for me and my children, after we’d tried so hard. However the experience had hardened me as I knew it was just inviting more manipulation into my life and at that point I had a severe SN child who I just had to prioritise. So I told DH I totally respected that he would want to live with his daughter again but that I had a line and I would not cross it again. Not without a lot of frank talking. I might have even been prepared to go to family counseling for 6 months and then see if she moved back in, after we’d sorted out some issues, but of course this was rejected.
Best decision I made for a long time. SD and her Mum were forced to have more of a relationship where the Mum didn’t just fob her off, and SD had to amend some of her harsher ways in order for her Mum to accept her living there. Her Mum doesn’t stand for crap! And in a way it was really the best thing for everyone.