If is it a separation by agreement, then you have a written one prepared by an attorney. Leaving without am agreement may give rise to a ground for a divorce. In NY you do not need a ground for a no fault divorce.
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A two week separation would not be considered abandonment. There should still be contact with the children. Good luck.
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I do not know New York law but I do not see how it is abandonment in any state. I would make sure everything is in writing and that during the separation you are seeing your children.
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