Lwaxana Troi had always known that she was a woman who would kill to protect her children, if it were necessary. But knowing it, as a safe abstract when your daughter was, if far away, perfectly capable of taking care of herself, and your son was asleep in your arms, his warm baby dreams a whisper at the back of your mind, was a lot different than really knowing it, the way you did when there was a Jem'Hadar soldier and you had to shoot him or your son would die.
She didn't hesitate, but she made sure that she felt every moment of his death – his surprise, the burst of pain, the quick fading away. Not to gloat, or to be sure that he was dead, but so that she would remember. She had killed a man.
Once she had killed to protect her son, it seemed a smaller step to kill to protect her friends, her home, her planet. She, and the rest of the resistance, tried their utmost only to do it when there was no other option. Still, the first Jem'Hadar she killed was not the last.
This was not the Betazoid way, but a man had threatened her son. She tried not to think of it in terms of revenge. She tried her hardest not to hate them. She just wanted them to be gone.
It was about being Lwaxana Troi. She was a woman who would kill to protect her children. She was not a woman who would enjoy it.