Give her plenty of positive feedback every time you "catch her out" being good. Often these kids feel criticism keenly but get little to no praise (often because there's little reason to praise them). For example, she eventually stayed in her room - praise her for doing what she was told. Make that praise unconditional, too. So often we make all our praise conditional, we can't resist an opportunity to preach at the kids. And this can really get some kids down.
Example - "Thank you for staying in your room. I'm glad you finally did what you were told. I wouldn't have had to send you to your room if you hadn't been difficult in the first place."
While technically you did praise the child in this example, it was conditional. The end result - it doesn't feel at all like praise, it feels like more criticism.
A better example: "Thank you for staying in your room. You can come out now."
That is unconditional.
Few parents have ever failed to lecture their kids enough. If asked, most adult kids (PCs) would say they got too many lectures that went on for far too long.
If you can give her some unconditional positive attention I suspect it might help. Your 3 yo is your bio child I gather? That could be another source of friction. However, don't assume miss 10 dislikes her sister - kids of that age gap, especially sisters (don't know why) often clash loudly, but love each other to pieces especially as they get older.
I was the youngest of a large, wide-spread family of mostly girls. One of my sisters (a sort of middle child) really copped it especially from the younger ones (including me, being coached by the older twins). We were really horrible to her. She was also a prime target because she could throw some amazing tantrums. If I had been asked as a child I would have said I didn't like her much and I didn't think she liked me. I remember she had to share a bed with me while I was still bedwetting, so I remember her getting angry with me at times. She is ten years older than me. The twins are seven years older. But now - we are all close, although my "middle sister" is perhaps the one I feel closest to. She is also the one my father would turn to for advice, including financial advice. Even though she is not the oldest, and we have two brothers who are older.
So never underestimate the tightness of a blood tie, especially over time. However, given the age gap now plus the problems of the older one, you need to keep a close watch on them and ensure a lot of supervised, structured play. Don't just let them each do their own thing without you actually being involved. You need to be there, playing with them. Make sure you give special time to the 10 yo because she's older ands therefore more able to handle the more advanced play. Find out what she wants to do - play a card game maybe? At 10, she can play quite sophisticated card games while the younger one, if she's advanced, still can't do much more than "go fish".
I recommend you teach the older one some more advanced card games (at 10 we used to play gin rummy, or whatever you guys call it) and then try to keep her involved in a game, with you too, teaching the youngest one to play Go Fish. Keep the Fish game short and try to leave a game on a positive note.
Encourage their dad to do this too. Family time is especially important in a blended family.
Marg