L.H.
You don't mention if your husband has had any input in this situation. Have you talked it over with him? What does he say about it? Has he tried talking with his daughter or is it all coming from you? If he hasn't done anything about this behavior then it's time for him to step in, especially since it's causing trouble in your marriage. It shouldn't all be on you.
It sounds like the step daughter is feeling she has to compete for the affections of her father, and the only way she knows to do it is to cause trouble for you and your daughter. She may not have come to terms with the break up of her mom and dad and may think consciously or subconsciously she can get them back together again if she breaks up your current marriage.
Your husband needs to spend some time alone with the daughter. Talking to her and having some fun together. Also letting her know that her behavior is unacceptable.
Also planning fun things to do with all of you together outside of the home would be a good idea. Or even some one on one time with you and the step daughter. Just make sure your own daughter understands that you are just trying to get along with the step daughter and not preferring her over your own daughter.
Who knows what this girl is experiencing in her home life. Her mother may be bitter and passing this on to her daughter. Maybe the daughter feels if she is nice and gets along with you and your daughter she is being disloyal to her mother.
I don't know if you are a praying person, but certainly pray about this. Pray for the girl's attitude and also that your own would be to help this girl figure out how to change her behavior.