Here are several resources about hardship licenses in MI:

Michigan Drivers License Suspension – The Hardship Appeal

Michigan Drivers License Hardship Law - Drivers Hardship License Law - Automobiles

SOS - Driver License Restoration Appeal to Circuit Court

I don't know if ANY of that applies to a child support suspension so you might be wise to consult with an attorney who knows about this sort of thing and see if there's a way to streamline the process.