"should a woman who travels to Syria to support and encourage 'JIHAD' against the 'West' deserve to live……………….?"
Does she deserve to live? I don't think the US has the right to execute her, if that's what you're implying. Unless there's some damning evidence I'm not aware of. But she sounds like a brainwashed propagandist, not a killer herself.
Totally fine with her being expatriated though.