Teens are weird generally, and unfortunately yours has some considerable trauma and a lot of big feelings to deal with at a time when she's too young to have the skills needed for that.
You're right that you were entitled to move on, but in doing so you've added some things into the mix that are hard for your DD.
When she started spending more time at grandparents and kicking off when you were pregnant, it was an attention thing. I'd guess that what she wanted was for you to 'fight for her,' to tell her she couldn't go there because you wanted her at home and you missed her. It may not make sense to you as an adult, but things are very different when you're 14.
And now, you're trying to be a mum to all your children and while blended families can work, your DD is watching her siblings enjoy a good relationship with their mum and dad, together, and that can stir up all kinds of jealous feelings - and they manifest themselves into angry outbursts and being a PITA.
Again, not rational or even your fault, but at the same time you can't really blame her.
How much does she know about her dad? Does she know he was abusive? Because knowing that makes up part of your dna is hard.
My guess is that she feels 'outside' of the family rather than in it. Her siblings, you and your DH are a family and she's on the outside, desperately wanting to be part of it but having no idea how to make that happen with all the feelings she's dealing with.
To address this, I would start with the basics. Have a talk with her in which you make it clear that you like and love her as a person. You miss her, you want her in your house and on the holiday. Be specific about why you love her, what her good points are.
Then deal with the behaviour. It's separate to who she is (the classic "I love you but I don't like your actions") and set out some family ground rules.
This should go some way to letting her know what you expect, but it also brings her into the family, because the rules apply to you, your DH and all your children. Together.