You're talking about two different things here.
The first, is basic child support. A step-parent is NOT legally required to provide
any financial support to his/her step-children. Period. The legal obligation falls on the child's legal parents...and if Dad isn't paying, then Mom (or CSE) needs to be filing contempt against Dad for non-payment (assuming there is an order for support).
The second, is state aid. The state looks at the
household income - not just the income of divorced Mom. That's what has happened here - the state has decided that you make too much for Mom and her kids to qualify for that help. If you don't want that to be the case, your options are limited...and include things like separation and divorce from your wife.
Your wife is also not considered to be a single Mom.
Sorry it's not better news (as far as you're concerned) - but yours is a common issue faced by thousands of step-parents every day.
(I'm also a step-parent, for what it's worth

)
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