I'm getting married in Ohio but live in MI. Can I be forced 2 pay my new husband's back child support on kids that are not mine?

Your finances are your own unless you somehow agree to make payments.   But your new husband can be made to pay back child support and money in a joint bank account might be directed to make his payments. I do not recommend putitng your earnings in a joint account until you are sure the friend of the court or whoever is controlling the child support payments gives you a writing that they will no sieze your funds in the joint account.