He can't claim her. Period. She did not live in his house for "more" than half that year. There's other things too. But they don't matter at this point. If he does claim her, he's breaking the law and the IRS will have a field day fining and penalizing him, as well as garnishing his pay from whatever job he may have. Also, go back to the court that ordered the child support. You can have his tax refund garnished, and paid to you directly. Might also even be able to get a portion of any paychecks he receives garnished too.
Now in cases where the custodial parent is going to allow the non-custodial parent to claim the child, the custodial parent has to provide a signed 8332 to the non-custodial parent.
So a lower court judge can very well order the custodial parent to sign the form, and hold that parent in contempt if they refuse. But a lower court judge does not and can not over ride federal tax laws.