It depends on several factors. If this was a case filed by the Title IV-D (Child Support Office) then they have the right to continue pursuing the case even without the cooperation of the mother. The child support office could be involved in the case if the mother had received certain types of public assistance.
If she filed the case privately and is not pursuing it, then you could ask that the case be dismissed for her "failure to prosecute"
If the other party does not show up and does not get court permission to continue the matter then you ask the court for what you want and you should get it.
The other person may ask the court to open the judgment, or they may start the case over in certain matters ( in most states child support is one such matter) but as of that time the judge should do what you wanted done in the case. If you are the only party to show only your evidence can come in.
This not legal advice which can only be given after a full disclosure and discussion regarding your particular situation. Any answer or comment by the attorney des not create an attorney client relationship and is not protected by privelege.