You can get a copy of the dismissal order from the court. You should get a certified copy of the dismissal. Your wife is probably entitled to petition the district court to seal her criminal history. she should definately do that if she is eligible. Until her case is sealed however, she probably needs to answer yes to the question of whether she has ever been arrested. I would recommend getting her an attorney that specializes in immigration matters before she turns in her application and to petition to seal her arrest as soon as possible.
Your biggest issue at this point should be getting an immigration lawyer. While the case may have been dismissed your wife’s record will show that she was charged with the original Domestic Violence charge. The charge alone is going to have ramification on your wife visa.