Can my husband's ex-wife take him back to court for more child support based on my income now that we are married?

No. Your income cannot be redirected toward your husband's children he had by another woman. However, a judge may take into consideration your husband's ability to pay in light of his present circumstances. If, for example, you are the primary bread winner and earn substantially more than him, a judge may rule that his lifestyle will not be significantly changed by paying more child support.