I am sorry that you are going through this. Your question raises many good issues. the main issue for your husband is whether he has any type of bar against his status and whether or not the crime he committed rises to the level of moral turpitudue such that it would affect his ability to adjust that status through marriage, please work with a local IMM attny, there are so many great ones in AZ. take care and best of luck.
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Your husband needs to hire a lawyer who can help him quash the warrant and defend him in the case he never went to court for. He must try to resolve that case with a non domestic violence designation in order to have a chance at obtaining a visa.
I would be happy to provide a free consultation on this.
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I would recommend that you repost your question directed to the Practice Area of Immigration. That will increase the likelihood of responses from attorneys with experience in this specialized field. Good luck.