Is the wife obligated to help her husband financially in paying off his debts and the expenses of their children, especially since she feels exploited and that she is the primary breadwinner for the family?

Safety is in God's hands, and we advise you to turn to Him to mend your situation and grant you safety. We also recommend that you draw closer to your husband, think well of him, and seek reward from God for what you provide for him and his children. This should not prevent you from demanding your right to maintenance from him in a reasonable manner. What you provide for him can be considered a loan that you can reclaim when you need it. Know that a wife's going out to work is contingent upon her husband's permission, unless she stipulated this in the marriage contract. The husband is not obligated to provide for your child from another man.