You don't need a checkbook to get money out of a joint account. Just go to the bank with the account number and request an ATM card for yourself and new checks. You can also withdraw money from a joint account.

But once you do that, expect it to be closed.

What you need to do is contact your local social services, they will be able to tell you which agency collects child support. You then contact them and get everything set up. And ask that it is automatically garnished from his wages.