I think that's much better. I would just try and make "Long on the run from her powerful father after an attempted rape" a little more succinct. Too many big adjectives in close proximity.Who knew loggin' was such a deep subject?!
Here's the latest
Long on the run from her powerful father after an attempted rape, a young woman turns to fight when her recurring nightmares reveal the truth about her mother’s murder.
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Or you might want to add another layer of drama in there:
"A young woman promises never to go back home after barely escaping a rape at the hands of her father, but she turns to fight when her recurring nightmares reveal the truth about her mother's murder."
I don't know if that matches up with your story, but now you've got her breaking her promise to herself, and the fact that she barely escaped the rape. You don't need to say that the father is "powerful." It's enough to say that he tried to rape her.
I would only include "powerful" if the father is well connected, as in police / judge connections, in which case that would require more explanation.