But either way, if he has some kind of court order that he could claim you and your sister, or if your mom gave him written permission, then he legally could. Not paying child support doesn't affect that.
If your parents are still legally married but just living separately, it's posssible that your dad could file as married filing separately and claim an exemption for your mom.
So depending on circumstances, there might be no fraud and nothing to report. But if he is not entitled to claim any of you and he is, then yes you could report him to the IRS. It wouldn't benefit your mom, but wouldn't hurt her either.