回复：信上说 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.

你给你前夫带来了大麻烦，那个是criminal case, 会影响他以后的工作和人生。

关于你的问题，如果你前夫的案子定案， 是，你可以以domestic violence 申请永久拘留。不过，劝你三思而后行，这样的男人够宽宏大量了，否则他完全可以送一封信给移民局，说你是诈婚，到时候麻烦更多。