Good for you for reaching out for ideas and support! It's so frustrating when we see a child who has just been hurtful walk away, looking like they don't care. But don't believe it for a minute!
When children have done something hurtful, a feeling of guilt floods their system immediately. Guilt paves over every tender feeling a person has. They immediately feel distant, separate, and lose all sense of connection to others. It's this way for your stepdaughter, and it's this way for all children.
When a child feels guilty, they can't cry, can't show upset, can't show affection. So others around them are convinced that they don't care.
Because she's your stepchild, the steps toward helping her might take awhile...most stepchildren have been through a grinding separation from one or both of their parents, the emotional upheaval of all that, and have had to make new relationships without really getting to choose those relationships. So it's a hard road, emotionally, no matter how warm and close your family might be after all the hard part has passed. Emotionally, there probably is some recovery she needs to do still, some feelings locked inside that she doesn't know how to tell anyone about.
When she's feeling particularly out of control of her life, or distant, or sad, she loses her will to be kind. Her mind shuts down, her feelings shut down, and out pops difficult behavior. She doesn't really want to be this way. But she has to signal that things are off-balance in her midbrain, the seat of her emotions, and like all children, she signals through her behavior.
Here's a way to help build the trust she would need in you to be able to tell you more about how she feels, instead of hurting others to signal that she's hurting inside.
Try doing Special Time with her. Set aside some time (and say how much money can be spent, or whether you have transportation or not), and tell her that she can do whatever she wants in that time with you. Be warm, be interested, and see what she wants to do. Be pleased with her, enjoy her, offer more eye contact and more warmth than usual, and don't multitask or bring up sore subjects AT ALL. This is "warmth time"--you're trying to give her the connection she needs to be more loving.
Don't be surprised if, toward the end or at the end (you need to time this, so there is a distinct end of the 20 minutes or hour you've set aside for her) she finds something to get upset about. That's how it works. You offer warmth, she feels the warmth, and then, she tries to signal that she has some stored upsets that she wants help with.
If she starts to get upset, stay with her. Here's one story of how Special Time worked in one family:
There's more about this at the website below. This strategy is a good way to begin building a relationship with her that will allow her to offload the hurt she carries on the inside, so she isn't driven to hurt others on the outside.
Again, good for you for reaching out for some assistance: it's not easy being a step-mom. It's good you care. She's fortunate to have you in her life.