Behavior is usually purposeful. children would act out even to get negative attention.
It may be possible that now that her step dad is no longer present, she is trying to test her limits with you. Another possibility for her acting out is that she may be fearing that now you will give more attention to her brother instead of her. Therefore, she is acting out in a negative way that seems to be pushing you away where in fact she may be wanting some attention because she loves you and is afraid that she can lose your affection and attention.
You may want to try a different approach with her. Try to engage her in some bonding activities, allocate some responsibilities to her, find out if there are some things that she would like to do just with you and compliment her and praise positive behaviors (even the smallest things)
If you feel that the situation needs professional intervention, family counseling with her may be something to look into.
Her behavior seems clingy. She may not be paranoid but rather anxious and that comes out as self doubt further seeking attention from you.
You may let her see that since you and her do not consume your time taking about others all of the time, it is most likely others are doing just the same.
Remind her that people may say what they wish and that she can try to earn good comments (which depends on her actions)
You said it is hard to give her what she needs when she's pushing you away (that may be one of her ways trying to get your attention and more time for herself. Try to spend some mother daughter quality time)