A complaint for modification of child support will require both parties to file financial statements. The latest version of the financial statement has a line to show contribution from other household members. This would include a spouse or a roommate if they pay a portion of the household expenses. The financial statement is suppose to show your complete financial situation. If your rent, mortgage, food bills, or any expenses are paid by another person, they need to be shown on your financial statement to give a complete and honest financial presentation. However, your spouses' income that is not used for expenses does not have to be shown. On the other hand, you may have to reveal their income in discovery if documents are requested or other information is sought. An example is a joint federal tax return would have to be produced and would show your spouses income.
Your new spouse has an obligation to support you but not your children. If the new spouse earns enough income to support themselves and you, then the court can consider their income to the extent that it allows you to pay more money to support your children. If this argument is made, then your new spouses' income must be revealed. The rest of their finances should not need to be disclosed.