In the state of GA does the step-parent have to pay the support of the child of the biological parent when he is not working? The step-parent is the only one handling the household.

To conclude my question I also have two kids of my own and they are not my husband's biological children and they live in the house with us.

The step-parent has no obligation to support his step-children.

The issue here is that the non custodial parent needs to go back to court and get the support reduced if they are not working.

The step parent does not have any liability to pay. Of course that does not stop them from arresting the non custodial parent for non payment, so if the step parent does not help pay.

So being that I'm the only one working at the time they won't come after my wages for his child support of the child that lives in another state?

... they won't come after my wages for his child support ...

Correct.

Thanks everyone for the help