You need a State court order. There is no other way. The IRS will not let you have this information. Only a State court can force your ex to produce it for you.
Mr. Larson is correct that this is a state law issue, and the IRS is prohibited from providing you with your ex's tax information without a signed release (likely IRS Form 4506-T). From your facts, it seems you ex will not sign such voluntarily. Accordingly, you will likely need a state (family law) court order to compel your ex to provide such.
This is private information and not available to you without a court order or authorization from your ex.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
The other answers are correct you cannot require the IRS to give you anothers tax return without a Court Order or an authorization from that person. However, I think your underlying problem i.e. child support not being calculated correctly because he refuses to cooperate is a different issue. You could hire a lawyer but fortunately in Michigan we have the Friend of Court which should help you get the correct amount of child support. If you have opted out of Friend of Court Services you should immediately opt back in by filing a motion. Next make sure you set up an appointment with your caseworker and let them know your concerns. Finally, if you know he is working find out where and ask the judge, by way of motion, to sign a subpoena for the checks or cash they have paid to your ex. Good Luck!