the process was so different when your mother applied to college, decades ago. Before you get a penny, your information now has to be verified by the IRS. So is your mom now talking about trying to defraud 2 federal agencies? this will not work out well and you will be the one to suffer.
If their combined income is less than 110k, you will be eligible for an excelsior scholarship. Tell the truth, take the student loan if you have to in order to attend CUNY, but don’t close doors on your future unnecessarily.