i would think Corey would be able to go to court for a reduction of CS based on his income, or lack thereof. He also can probably petition the court to have the CS dealt with by the CS office where they could either (1) put it into an account that is used for expenses related to the kids (2) or garnish his wages directly, therefore proving he paid the CS and she cant claim poverty. I would also think if there is a question of spending, he could petition the court to ask for bank records showing the CS is going towards the kids.
If he were to go for reduction of child support, she would have to come with her tax returns from previous years and recent pay stubs. I am nto sure how it works in NJ, but both parents income is calculated into CS and if the majority parent makes more than the noncustodial parent, the courts will not make the noncustodial parent pay huge amounts. Its all a calculation of income, percentage of time with the children, expenses, etc.
I think if corey can prove she is making more money and he has little he can request a reduction. I also think if he believes the CS money is not being spent on the kids, he can petition the court.
Also regarding alimony, i dont think they were married long enough for either of them to get alimony. Usually state minimum is 10 years and 10 years you get 5% with increases in every few years of marriage.