Personally, I think my dandruff is caused by a history of eczema, shitty New York tap water, and chronic bad juju. After my traumatic episode, I searched the racks of Duane Reade for any type of drugstore-brand scalp treatment, when I came across a familiar face: tea tree oil.
From Midtown or the Village, take the F or D trains that run down Sixth Avenue from Central Park to Washington Square or the N or Q trains that run down Broadway to Canal Street. All four of these trains will take you directly to Coney Island in Brooklyn.
Instead of taking the Amtrak all the way through to Newark, I would get off in NYC and take the NJ Transit train into NJ. Amtrak stops at Penn Station and the NJ Transit train also stops at Penn Station. Hopefully you won't have big pieces of luggage with you. Have your family pick you up at the nearest train station. Taxi fare from Newark Penn Station to Saddle Brook will probably run you $75+.