Right, now "pirategate" is over with, I can focus on my own life!
Back story; DSD (14) has been estranged from DP for 18 months, after giving him an ultimatum to choose between her and me. We'd been together for 18 months, and had moved in together a matter of weeks before DSD "voted with her feet" and refused to have any contact with her Dad.
All this happened against a backdrop of active alienation by her mum - who disciplined DSD if she chose to see her Dad - despite a court recital giving her the choice. DSD and her mum were BFF, and DP and I were the bad guys. Fast forward a year, and things are not going quite so well between DSD and her mum; reports of screaming matches, public arguments on FB and teenage tantrums. This culminated in DSD getting in touch with DP out of the blue one morning, saying that "she needed him to be her Dad". He met up with her and it transpires that one of the many rows with her mum had ended in DSD being hit.
DSD decided that she wanted to stay in touch with DP - and after a lot of soul searching, he told her that he thought that would only work if they "dealt with the elephants in the room" - in other words, they didn't ignore the last 18 months, they gradually got to know each other again by talking about the issues. she agreed 
One of the biggest issues is me, and although DSD wanted to address it straight away - DP sensibly suggested they deal with other issues first - like the fact that DSD thinks DP was mean to her mum when they separated, and that DP broke his promise to DSD when he moved out (he told her she could live with him, but she remained living in the family home with her mum).
I have agreed to give them some space and committed not to be around when DSD visits our home (at the moment, weekly, for a couple of hours) so that DSD doesn't have to worry about seeing me.
Things seem to be going well - DSD is using DP as an outlet for the stress with her mum, and DP is able to talk her through situations without criticising either her or her mum. He is approaching it from the pov that he is developing a relationship with an adult, but one who he is happy to share his experience with and one who he gives some leeway to in terms of language and behaviour because of her age. DSD says that she is still subject to pressure from her mum about seeing her Dad. Comments like "oh, so you're going, then?" when she says that she will be late home, and demands to know what they talk about when she gets in. It is an indication of how much DSD relationship with her mum has deteriorated that she is prepared to continue contact with DP despite her mums active disapproval.
As for me - I'm coming round to the idea. At first, I was horrified at the idea that I might be expected to accept DSD back into my life. It will take a long time to get over the hurt she caused me and DD; and I won't allow her to be a pat of DD's life again for a very long time, if at all. But, now I can at least imagine a time when I will be comfortable spending time with her - which is progress from where I was a few weeks ago.