It's a good present, and you sound a nice family. The problem is, you have two people's income meeting the baby's needs, and one person's meeting the teenager. And however you manage that, the disparity will show - I don't mean, necessarily, in actual money spent - but the level of thought and hesitation, when buying things for each. My mum was a single parent on a really tight income, and the tension was there, even if she didn't voice it, because she had to watch every penny. It wasn't there with my Dad, as he was far better off (helped, I found out as an adult, by his never having paid a penny in child support!), but I always knew which parent cared most. I knew why she would hesitate and consider, so I never minded. But your DD hasn't got that. She doesn't know.
You have to put thought into her provision, in a way that's missing from things you get her sister. And she has no way to know the dynamic: DP happy to contribute, you not feeling that's right, so less money being available from your principles, and not any reduction in the love. But she may well see you getting things for the child with double the money coming in without second guessing, and know that you don't do that with her - and she won't know why. You mention being extra careful right now because of maternity leave - but you don't need to be as careful with the baby, because DP's not on ML, is he. It will show in your attitude, and she may well notice that since the baby came, you're even more careful in spending on her, when you aren't on the baby in the same way. I would have.
Personally, I think you need to do one of two things: talk to DP about fully combining finances so DD doesn't feel like the stepchild, however much you try to hide it; or explain to her that he's happy to pay, but you take pride in providing for her yourself, as you've always done, and that is why you need to be careful financially - she doesn't get less (car seats are safer when you spend a bit more, and easier to manage - she'd have got that one too!) but you do need to plan your spending with her, as there's only one income behind it. You can explain that it was her and you so long, you don't want to change that responsibility as you take pride in it - at always providing for her. You can do that in a way that makes her feel valued, or you can change arrangements so the income to provide for her is doubled, but I do think one or other needs to happen. Because it may not be about money per se, but by how much more relaxed you are about spending on her sister. She has no way to know that there is a bloody good reason for that, and it has nothing to do with favouritism - so change the income stream, or tell her the truth. That would be my advice.
Having said all that... she's also going to be vile sometimes because she's 15, and that's the job description! So really, she's just doing her duty. 