Legal Question in Wills and Trusts in New York

It should.

Yes. If they are not mentioned they can contest the Will. Suggested language might include "I have intentionally left nothing to my children "X" and "Y", for reasons they know", or "I have intentionally left nothing to my children "X" and "Y" as I have otherwise provided for them", or some similar language. This is a response to an Internet question and the reply is not intended to be legal advice or as creating an attorney-client relationship.

You should discuss strategy with an attorney, possibly considering the use of a clause leaving a nominal amount to the children, and providing that, if they contest the will, they would receive nothing. A large estate could be seriously depleted by claims made by disinherited heirs.