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.