Therefore, holding herself in check in situations where violence is an unnecessary temptation would decrease her Addiction/Obsession obligation. This would reflect the evolution of her PC as she gets herself under control.

I think "unnecessary" may be the key to making this work. Engaging in violence when it's "legitimately" necessary probably shouldn't negatively impact the character's obligation (Though that may not be realistic - if someone held a gun to a habitual binge drinker's head and forced him to drink a few shots, I don't know that it wouldn't still trigger a binge -- with a player who is looking for combat, you don't want to totally disincentivize combat).

Give the character opportunities to start unnecessary fights and when she does, increase obligation by a point or two and when she resists the temptation, reduce by a point or two. There's no need for huge swings either way.

In sessions when the obligation is triggered, she is feeling the itch -- have her roll a Willpower or Discipline check if she wants to resist the urge, but leave those checks out when she isn't triggered.