Welcome to Essex and Morris Counties.
For train information, I suggest you check out New Jersey Transit and the Essex/Morris Line, http://www.njtransit.com,
to determine how long it will take you to get in and out of the City. The train ride to and from Short Hills/Millburn is shorter than that from Chatham, but not by much.
As far as pre-k programs go, there are many to chose from and times vary. For working families, you will find those that offer extended stay programs.
So you know, I am a long time resident of Chatham, 25 years, and work in Maplewood, the town next to Millburn/Short Hills.
Feel free to contact me with any other questions you have regarding these lovely towns.