Boy, does this sound familiar! I came into my daughter's life when she was 8 yrs old. We also do not use the "step" as it is a 4-letter word. My daughter's mother has Paranoid Schitzophania (sorry for any spelling errors) and so things were not great when she was small. Actually, my daughter did not have most of the skills necessary for her age because so many people felt sorry for her and did everything for her. There were times when my son, who is 7 yrs younger than her, would help/teach my daughter how to do some things.
I happen to have a long family history of "borrowed" children and parents. My daughter and I make it 5 generations actually. All of us are 1st daughter to our fathers. So I knew what I was getting myself into in the 1st place. These families are not rare anymore but they can still be difficult, for all members!
Take some time where both you and your husband can sit down together with the 2 oldest children (I am thinking the youngest is still too young to be included yet) and then with each of them individually. The four of you should discuss what it is you all expect from each other and be blatantly honest. Warn your husband ahead of time cuz most men need a heads up otherwise they get upset when you are that honest in front of children in general. LOL!
Then give your new or "borrowed" daughter time 1st and say to all that it is in order of age at this meeting but next family meeting it would be reverse then keep to it. Tell her that NO truth is a bad truth. Make sure she understands that even if you don't like what she has to say, you still want to hear it. This sets up a nice line of communication so that when you have to say something to her she doesn't like to hear, she knows you are not "picking" on her cause she didn't come from your belly like the other 2.
Just don't make an additional issue with your birth daughter by not giving her equal time and attention in all things. Ask boths girls evenly for things to do and help you. Maybe giving them a chore a few times a week that they can do together but not by themselves will help with their bond.
Also have "Momma and me" time alone with each child. Your husband will also need his "Daddy and me" time with the children. Friday nights I spent with my son and Sautrday mornings I spent with my daughter while still leaving Sunday mornings for just plain ole "ME" time (I didn't have an issue with getting up super early before the others stirred out of bed). My husband would then have the opposite times but no official "ME" time cuz he worked outside the home and could take his after work with his friends/co-workers. It never mattered what we did during these times, we even sometimes just watched the same t.v. show while sharing a soda and popcorn on the couch together.
My daughter has called me "Mom" since she was 11 yrs old. But have always made sure she never said it in front of her mother. She called me Aunt D then. I could never inflict pain on another mother like that even tho there were many problems between them (even after she got help). Always insist, as best as you can while still making sure she is safe, that your daughter spend time/talk on the phone with her mother every week. This will tell your daughter in actions that she still has her mother but now she has an additional one that will help her along the way. Course, I am still the 1st phone call when my daughter needs advise/help at her grand ole age of 22. LOL!
I hope I haven't confused you with my phrasing of how we, in our family, refer to each other. Gosh this is hard to write - much easier to say in person. LOL!
Please feel free to send me a private message on this group if you have any questions. Since I have dealt with and have come out the other side of what you are dealing with now.