I know where I live you can go petition for C/S without having to do anything else legally, such as filing for S or D.
You could go to the internet and figure out the percentage your H would have to pay in C/S in your state and contact your H with the figures and see if he'll go along with that before going the legal route.
Contact about kids or financials are a legitimate reason to break N/C. As the primary breadwinner your H is legally obligated to financially support his children.