If your husband's income has decreased, or his expenses for your children has increased, it would benefit you to file a Petition to modify the Child Support Amount, explaining in his Petition the "Change in his Circumstances" which is the factors which Jdges use to increase or decrease child support amounts.
No one can stop your husband from signing a "Voluntary Relinquishment of Parental Rights"; however, doing so would not relieve him of the obligation of child support.
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ANDREA, JD, LL.M., Taxation
Member, NY & PA Bar
DISCLAIMER: The facts stated herein are information only and are not intended, nor should be construed as legal advice or legal opinion and No Attorney-Client relationship is formed by asking questions and receiving information; laws vary from state to state and to protect your interests, you should seek local counsel