conviction of domestic violence is a ground for you to lose your green card next time you try to renew it.
You know you are guilty, your only way out is to be convicted to a lesser crime and still keep your green card.
Whether your wife's injury really resulted from your assualt is not the point, the point is that the district attorney can prove that you hit your wife. Your wife has injury, and there are probably witnesses to your alleged action, that's enough to convict. It's all about evidence.
Get a criminal lawyer.
