Not exactly. In some states you cannot legally cut your spouse and/or your children out of the will.
True. it's called an "elective share" - a spouse can elect to take some portion of the decedents estate (usually around one-third), in lieu of what is provided for them in the decedent's will. If I remember correctly, in New York, it applies only to one's spouse, though in other states it can apply to children as well.