As the non- custodial parent, when you remarry, your new spouse does not have a legal obligation to support your children from a prior relationship or marriage.
RCW 26.16.205 (Liability for family support – Support obligation of stepparent) provides: "The expenses of the family and the education of the children, including stepchildren, are chargeable upon the property of both spouses or both domestic partners, or either of them, and they may be sued jointly or separately. When a petition for dissolution of marriage or state registered domestic partnership or a petition for legal separation is filed, the court may, upon motion of the stepparent, terminate the obligation to support the stepchildren. The obligation to support stepchildren shall cease upon the entry of a decree of dissolution, decree of legal separation, or death."
The statutes are at http://apps.leg.wa.gov/rcw/default.aspx?Cite=26 .
If you look at the pattern child support worksheets, each parent is required to provide the income information for all adults in the parents' households. That is, you need to release the information about your new husband's income. The pattern forms for most WA family law proceedings are free at http://www.courts.wa.gov/forms/ .
In theory, the court can consider the incomes of new spouses in determining the child support amount. Whether the court would consider your new husband's income in your case depends on facts not given in your post.
For example, let's say you have been making about $60,000 a year and married someone who is financially well off. You stop working and ask the court to reduce your child support. Not only the court would not reduce your child support amount, the court likely would use quite a bit of your new spouse's income in setting a higher child support amount for you.
As long as your income does not go down from what it is before the marriage, the court likely would not have any reason to consider you new spouse's income.
You can review the specific facts with your attorney to see how the laws may apply to your case.
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