The way I see it, I don't think tormenting the Doman people was what Yotsuyu wanted most. I think what she wanted was to kill her family. Since they were protected through Garlean citizenship, other Domans were the next best thing. She rationalized this by thinking "Well, none of them helped me, so they all deserve it." But after she killed both her parents and Asahi, she was at peace.
(4.4-5.4 SPOILERS)
Personally I'm not really a fan of how they ended her story. What she did was awful, but it felt too mean-spirited to kill her off like that when she had a chance at healing. Especially since Gaius got to walk free, even though he allowed Ala Mhigans to be enslaved (Radiata) and possibly looked the other way when his soldiers abused women.
I wonder what would've happened if she lived, though. She'd probably be tempered, and she definitely wouldn't be able to go out and about, so she'd need to be kept somewhere safe. After 5.4 they'd be able to cure her. Not sure what would happen after that.