There are attorneys out there that help with immigration. Your soon to be ex sounds vindictive and spiteful in doing that. Sounds cruel and abusive in doing so. Why should filing for a divorce warrant such ludicrous behavior anyways?

Eta: the way it's described to me is-in regards to fear tactics is that the enforcement agency is primarily concerned with fingerprints in their system. Not to say don't be proactive and ensure all your ducks are lined up in a row so to speak but there's a backlog of priorities. Definitely speak to an expert but I really think it's a fear tactic some hurt soon to be ex spouses use whether that or threats about child services or calling employers etc etc