Wow, props to you OP for being so honest. I liked what cleansheets said too, nice to hear empathy from an adult DSD. Being a stepmum to a DSD of 5-18 years old is said to be the most difficult step family gig. And there is a halo / pedestal effect when a parent has died too. You're doing well though. Washing at 12 - OK, with help! We're still cajouling DSD at 16!
You will have to say things to your DP, but the line between what to say and when is delicate and ever changing. I'm highly sensitive to exclusion, fairness and respect too. Could you write to DP, validating his and daughter's experiences, sharing your own and saying what you'd like to be different too?
Don't be hard on yourself about "growing up", you're being mature and vulnerable which is completely natural, and responsible in assessing your place in it all. A dad's bond with a daughter is v special (although it's not good to favour a child over another, agreed). My situation was similar. Came into my DP's life when DSD was 11 and I baulked at some of their interactions. :-/
I get the impression you haven't been together long (a year?). If you can focus on where you're both going in the relationship, that will help. If you really want to be together long after the kids move out and you have a plan, great. If not, be honest with each other, you've got your own kids to think of too. If it is for the long haul though, what a wonderful opportunity you've got to be a maternal role model. I know that film Stepmom is quite cheesy, but I love the scene when mum and stepmum reconcile and they agree that her mum had the daughter's past and the stepmum had her future.
Men aren't always good at doing the emotional thing and bringing family members together either. So you could reach out more olive branches to DSD by smiling at her, showing interest in her life, offering odd favours to relieve DP etc. Then maybe you can all agree some house rules for the 5 of you. Make it fun and playful, stick it up somewhere. Do you all go out places and see each other in different settings, like theme parks, zoos, bbqs, restaurants, stage shows etc to break the ice and have a good laugh? Balance this with picking your battles, seeing your own friends / doing your own thing too.
But I do think your DP should keep telling his DD that it's OK to keep loving and remembering her mum, you're not replacing her, and it's OK to like you and grow closer to you too. We drowned DSD in this early on she was like "OK I get it!!"
, (mum's still very much with us sees DSD every day, so it was v important to emphasize this).
One thing I found worked well was asking my DSD for her permission / agreement that I could tell her when she was rude. I remember she looked pleasantly surprised to be consulted, but had an air of responsibility too. I've only had to pull her up about 3 times.
Remember she IS still a child and kids develop at different rates, as you've probably seen with your own. Go at her rate, she WILL start to come to you for stuff.
Finally couple of book recommendations, The Smart Stepfamily, Ron Deal and The Smart Stepmom, Laura Petherbridge. They are from a Christian faith perspective, but side stepping that, they are really good in general and practical terms. Reading The Smart StepFamily opened my eyes big time and helped me answer the question, "Knowing what I now know, do I want to go ahead with this marriage?" A big yes.
Good luck.