Procedure for seeking temporary custody of 18 year old niece, NJ child custody laws

Your question is somewhat complex for this message board. I don't usually say "talk to a lawyer" when I can avoid it and answer it straight-out, but... you need to talk to an experienced family law attorney. Even if you can't afford to retain someone, getting a consultation will be worth it (and, besides, there are a few of us who don't charge for them). Just make sure the attorney specializes in Family Law, not a dabbler or "Jack of All Trades", espeically with your facts.

You've got two primary issues- a non-biological parent seeking custody and interstate custody.

I can't really tackle the first on the facts you've given, but you certainly seem to have an argument (again - based on what you've said).

The second issue is more straightforward. Under the Uniform Child Custody Jurisdiction Enforcement Act (which every state has enacted) and the federal Parental Kidnapping Prevention Act (don't get thrown off by the word "kidnapping" - it's just a jurisdiction statute), NJ will have jurisdiction over this matter as of FEBRUARY 26, 2009. If you raise the custody issue before than and the other side files in Florida - you'll have to go there to defend it. As of 6 months residency, jurisdiction over the child should be in NJ (FL may still have to relinquish jurisdiction, requiring a motion down there, but under the law they should do so).

Keep your head down until 2/26 and speak to experienced counsel.