Her behaviour gets better occasionally - usually when she wants something! She can be an absolutely lovely girl, and we did used to bond over all sorts of activities, but she hasn't really wanted to be like that since she moved in, and obviously we have been encouraging her to get out and make new friends, so she has (naturally) wanted to spend less time with us than she did when it was just weekends. Getting your DSD involved in a sport sounds really good, sitting about at home for days on end does no one any good. I'm sorry if I sound negative Zxzx but that has been the reality of our situation - it went from looking forward to seeing her most weekends to a very different relationship once she was living with us, and the discipline side of things has been the most challenging. I would love to have kept things how they were, with us being friends and sharing cooking and going out doing stuff together, but she hasn't been even slightly interested in any of that since she became a full-time part of the family.
Updates I haven't got involved in managing her behaviour until very recently, when I couldn't take any more. I think now that possibly I should have got more involved earlier, but that didn't feel right, but when DH couldn't cope with it that caused problems between the two of us, and he felt "pig in the middle"...not great. The most important thing is for you and DP to be absolutely together on everything, teenagers are great at "divide and rule", but once they see that isn't going to work, it does ease up a bit!
I think I also had unrealistic expectations about how she would help with the baby and the house - as she had done when she was just a visitor - but it's very easy to be wise after the event; having lower expectations now mean I get disappointed less often, and our relationship is better as a result.
One thing we have found useful is to give her very fixed tasks to do that she can easily manage by herself - stacking the dishwasher etc - and keep to that so it becomes part of her routine; apparently it takes three weeks for something to become a habit, and that's just how it has worked. DSD also does her own laundry, partly because she needs to start to learn to look after herself (she is nearly 18) and partly because she expected me to do it but without her doing the rest of the family's in return...
Your plans for her annexe sound great, depending on how old she is possibly see if she can get a job so she can start buying bits and pieces to go in it.
Re the new baby and DSD, she wasn't very interested at first - after all he just slept and screamed - but now he is bigger and more fun she loves him to bits. Maybe see if your DSD will cook dinner one night a week whilst you put the kids to bed, and also help with the two little ones - especially fun things like bath time - as that will make her feel more part of the family as well, particularly as tiny kids return the love in buckets 