IfI recently got charged with domestic violence and my wife does not show up to court, does the state still have a chance to convict me?

Whether or not to prosecute a case (that is to drop charges) rests with the prosecutor and not with the a victim.  What that means, is that a case may be prosecuted over a victim's objection or assistance. While the state's case would be stronger with her cooperation, if there is other evidence to support the charge the case may still go forward.

That having been said, an skilled criminal defense attorney may be able to use the fact that she does not want to testify to obtain a favorable result for you. They may possibly be able to talk the prosecutor into dismissing the charge (or at least reducing it). However, prosecutors can be unwilling to simply drop these types of cases since they do not want offenders to think that that if they can intimidate a victim, they can get away with this behavior.

Additionally, if she has been subpoenaed she can't just not show up. A subpoena is a direct order from a court that a person appear at the place and time specified. If it is ignored, the person who received it can be held in contempt; a warrant for FTA (failure to appear) can be issued for herr arrest and she can face fines and/or jail time.

While some victims try to refuse to testify by invoking the Fifth Amendment (i.e. the right against self-incrimination), this right can't be invoked simply because they do not want to testify. This right only applies if their testimony would cause them to incriminate themselves. Further, in domestic violence cases, some spouse's think that they can invoke "spousal privilege"; that is the right of one spouse not to have to give testimony against the other spouse. However, the majority of states have amended their laws regarding spousal privilege to make an exception for domestic violence victims. Consequently, in such cases one spouse can in fact be made to testify against the other spouse.