I think that her reaction might be a little muted, personally. I think they definitely had Something going on, but Bari would also be someone who would respect what she would reasonably parse to be his wishes. And knowing how powerful and how much influence Don Quixote has over his Family, him being taken out or at least incapacitated by them would mean two things: 1) He didn't fight back, 2) He decided to not use his powers to keep them from going out into the world to wreak this havoc. So him allowing them to do as they pleased was his final wish.
I definitely think Bari would mourn him, knowing that he'd no longer be in the world with her anymore. Though that doesn't mean she'd also not go out of her way to punish his Family or seek vengeance if it was really his wish that they not be stopped from seeking their happiness unless she thought it would be too adverse for humanity, or against her own goals and ideals.
But if they did come after her, she wouldn't hesitate to put any of them down if they tried to take her life.