回複：信上說 we have been made aware that a domestic violence

That means DA has not filed any case against your ex so far. That does not mean DA won't file such a case later.

你給你前夫帶來了大麻煩，那個是criminal case, 會影響他以後的工作和人生。

關於你的問題，如果你前夫的案子定案， 是，你可以以domestic violence 申請永久拘留。不過，勸你三思而後行，這樣的男人夠寬宏大量了，否則他完全可以送一封信給移民局，說你是詐婚，到時候麻煩更多。