Your instinct is a good one. Do not mix the issues or create an opportunity to say "he's only motivated by the money." If the court hears oral argument on your motion to increase parenting time, the judge may bring it up on his/her own. If not, just wait until it's done and then file your motion to adjust support.
One word of caution - if you already had two overnights per week and her income was sufficient, you should already be on the shared parenting guidelines. The drop between 2 overnights and 3 may not be that much -- if you've had a raise since CS was last calculated, it could go up notwithstanding the increase in overnights. Check the guidelines before you file the motion. You can get a good idea of them from several websites and from the judiciary website www.judiciary.state.nj.us . Check multiple sources (assuming you don't want a consult where an attorney could run them for you) before deciding. Too many times, when it comes to "I want a child support review", people end up saying "be careful what you ask for.... you might get it."
I also suggest getting touch with noncustodial parents' support groups like www.facenj.org
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It is not likely that the judge will adjust child support without the formal request being made in your notice of motion. Once you get the additional overnight, wait a couple of months before filing so that you can establish that the additional overnight is a permanent change.
This answer does not constitute the establishment of an attorney/client relationship nor is there any guarantee that this advice will be completely effective in a court of law. A consultation, including review of court orders and other documents is necessary in order for me to give you proper advice and guidance.
I agree with the other two attorneys' answers. Even if you are granted the extra day visitation, it will not lead to any automatic change in your child support payments. For that you would have to make another application to the court to adjust your child support based upon "changed circumstances."
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