WARNING: The following article contains spoilers from Batman #122, on sale now.
Ravager has always had a difficult relationship with her father. An emotionally distant man at the best of times and an abusive parent the rest, Deathstroke's parenting style has not only damaged all of his children but in some cases driven them to seek revenge against him. Yet Ravager has always been different. While she holds animosity towards her father, she has never truly been pushed to go after him.
This all seemed to change in Batman #122 (by Joshua Williamson, Howard Porter, Tomeu Morey, and VC's Clayton Cowles). After being betrayed by Respawn and accepting that her father was about to upset the natural order of the DC Universe by proclaiming himself "King of the Villains" Ravager seemed set to kill him. She has even allied with Robin to pull it off. But after knowing him for so many years and coming close to having a somewhat normal family dynamic with him, can she actually pull the trigger?
Rose Wilson was the result of a brief love affair that Deathstroke had with a client of his, Sweet Lili. Rose's mother rightfully thought that it would be best to hide the child from Deathstroke, but he inevitably found out. From there it was a jarring pattern of interest and disinterest. At first, Deathstroke didn't want to be near her, not trusting his track record with his own children. Then, when both his sons from his first marriage were dead he manipulated Rose into becoming his apprentice, putting a fake hit on her just to provide her the opportunity to murder the man she believed killed her mother as a test.
Ravager would eventually break free from the cycle of manipulation and come to fear and loathe her father in equal measure. Despite that, she's never really had the courage to seek revenge, even after everything he had done to her. So her commitment to kill her father now is questionable. All in all, what Deathstroke has done to her lately isn't truly as bad as their earliest moments. Rose, of course, still holds it against him for abandoning their family after he tried to unite them again, a fact that actually brought tears to her eyes. If that was all it took though, then she would have gone after him much earlier.
The more likely reason is Rose has accepted that there is nothing redeemable in her father. For the briefest moment, she wanted to believe he could do good, only to be disappointed. Now he seems to be doing the opposite, not only trying to lead an army of villains but also murdering Ra's al Ghul and consequentially upsetting the balance of power on Earth. She isn't going after Deathstroke to settle a grudge, she's doing it because she believes it would be better for the world if he were gone.
Ravager's attitude towards it though is more resignation to an unfortunate task than a mission of great importance. It's understandable, as he's her father and a part of her loves him. On the other hand, she's also as much his victim as she is his daughter and those feelings are now coming into conflict. Rose's overall portrayal is one of defeat. Not because she has to kill her father, but because doing so eliminates any chance for a happy ending.
So the question stands: Can she pull the trigger? While she undoubtedly has the motives to do so whether she has the will is the question. She could very well be the one to end his life, in doing so sparing the world whatever trouble her father could come up with and leaving Rose with the knowledge that she killed her dad. It would also destroy any chance of having a relationship with Respawn, but in the long run, it might not be a terrible price to pay. However, her seeming exhaustion with the whole situation implies that Rose might let Deathstroke live, perhaps finally washing her hands of all pain from her past.