Domestic violence is not a charge, it is a tag or enhancer put on another offense, like disorderly conduct or battery. The complainant would not need to show up in court prior to trial. Whether or not their failure to show then would result in dismissal or not would depend on other factors, like whether there were other witnesses, or whether the accused made any admissions.
This answer is provided for general information only. No legal advice can be given without a consult as to the specifics of the case.
Attorney Witt is correct. The term "domestic violence" refers to the nature of the charge, not the crime itself. There are many crimes that will come under the umbrella of that term. Some of these are disorderly conduct, battery and criminal damage to property. As for what will happen if the person does not show up to court, there are several things that could happen. The State could dismiss, request an adjournment or request a body attachment for the Court to have the witness arrested for non-appearance (assuming proper service of a subpeona upon that person).
You should consult with experienced criminal and/or domestic counsel to address the matter as soon as possible. The implications of a domestic violence charge can be far reaching, beyond the disposition of the charge itself.