She ISN'T a child - she's a young adult, acting childishly.
I'm afraid, as you probably already appreciate, that the key to dealing with all of this is your DP. He has got to start getting real with this and effectively 'laying down the law' with his daughter because her utter lack of respect towards you is completely unacceptable.
Furthermore, even if she was, literally, an actual child - that sort of rudeness, hostility and (probable) spite would also be wrong. Kids (or at least kids who are parented responsibly) don't get a free pass on bad behaviour until the morning of their 18th birthday - yet this one is still being allowed to be a horror well past it.
IMO, your DP needs to sit down and TELL her that her completely unfounded verbal attack on you the other night - in combination with previous outbursts - will NOT happen again, or else she will not be welcome again until she learns to moderate her behaviour. I wouldn't care if, ostensibly, this was 'DP's home' ..... it is now your home as well, and if he thinks any differently - having made you pregnant - I'd be horrified and would be rethinking the whole relationship. As such, you're entitled to peace and respect from others in the house - just as you are respectful to them in turn. As you say, she doesn't have to like you ..... we don't hit it off with everyone in life ..... but assuming that you've done nothing unpleasant to her, basic courtesy should be a given.
I don't know if your DP is capable of laying down the law like that but it's essential that he does, especially with a new baby on the way. It would be awful were this to continue ..... I'd be concerned about her reaction to the younger child, and also about the message she'd send to him/her when they were old enough to notice (even subconsciously) how their mother was treated - and also, potentially, how their father allowed it to carry on.
This isn't about DP choosing 'sides' .... I'm sure he has enough love for you, his daughter and the new baby, but he has absolutely got to make it clear to her that such nastiness won't be tolerated any more. There's no foundation to it and I really can't think why she continues, unless she still harbours some hope of her parents getting back together and sees you as an obstacle .... it'd be interesting to know how she treats her mother's partner.
And regardless of how (undoubtedly) upset she was as a 7 year old when her parents split up 11 years ago .... there comes a time when for her own good, as well as yours, she has to start growing up and at least putting on a show of being civil. Basic manners, and no mouthing off, no damaging your things. DP needs to get tough with her if she objects to this and point out that she is supposed to be an adult now and is supposed therefore to be capable of adult behaviour - particularly while she benefits from being thought of as an adult, e.g. the car. He may cringe at doing this but sometimes you have to dish out the 'tough love' for a (so-called) child's own good - is he happy that his daughter is so foul ? .... perhaps because no-one's ever made her think properly about such behaviour and the effect it has on others?
It does sound as if your DP is very weak but only he can sort this out. Otherwise, what, exactly does he suggest going forward ? .... that you, and the new baby, should be subject to SD's sweary rants any time she fancies sounding off ? Does he really think you should just casually shrug your shoulders at that ?
Finally, am very sorry about your lost babies. That's another reason DP needs to man up and tackle SD. I've had several miscarriages and I know how scary each subsequent pregnancy can feel when you have a history like that. Furthermore, although there are all sorts of reasons for losing a baby, when you're under severe stress, it's natural to wonder if that's also played a part and easy to become very resentful if you feel your partner isn't doing all they could to protect you. I really hope you have no problems with this pregnancy but in view of the past your DP should by now be capable of understanding why it's so important emotionally - and perhaps physically as well - to ensure you suffer as little stress and anxiety as possible ...... and that means sorting his daughter out once and for all. That means telling her straight - and no, before he protests, he is NOT rejecting her, because she'll be welcome so long as she behaves like a normal decent human being, it means sticking to his guns if she continues to be nasty by refusing to have her in the house (and thus protecting you) and, it should also mean, that while/if she refuses to be civil, she does NOT get treated e.g. by him taking her out for meals or doing particularly nice stuff if he sees her outside the house. I wouldn't suggest he stops seeing her altogether, but there shouldn't be any element of 'reward' in those get togethers while she's determined to treat you with such disrespect.
Having said all that - two things have occurred to me. First, am not sure if she lives with you or not .... if she does, it obviously makes things more difficult but the basic premis should still apply. Either shape up or ship out. Secondly, is there any possibility that despite her mum still being with the man she left DP for, SD has been fed a barrel of lies about the circumstances of the split and the timeline and therefore 'hates' you based on a load of untruths ? ..... though am clutching at straws a bit there as she must surely remember you coming into her dad's life when she was 14?