no child support is a responsibility of the parent associated with the child not the new spouse. If there is a judgment for past child support, they can garnish bank accounts though.
Your new spouse is not responsible in any way for the past child support obligation that you owe. I agree with the above attorney that a joint bank account could be garnished if a judgment is entered against you, so that may be something you should look out for in the future.
This answer is provided for general information only is not to be construed as legal advice. This response is not intended to create an attorney-client relationship.
No, child support for your minor children is your responsibility, not your new wife's. The children are not hers, or her responsibility. In fact, should you and your new wife start a family that would be a basis for your support actually being reduced, since you would be legally responsibile for more children at that point.