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While a handful of states still recognize a civil cause of action against a paramour for interfering with a marriage, New York is not one of them. New York has abolished such causes of action, known as alienation of affection.
Adultery does continue to be criminal in New York (NYCL Penal Section 255.17) as a misdemeanor offense, but is rarely ever prosecuted. You can try to refer the issue to the state's attorney for prosecution, but both the woman and your husband will be exposed. And, there is little chance the crime will be prosecuted.
The court is largely unconcerned with the adulterous behavior in terms of the property distribution and alimony awards. Alimony is based on the relative need and ability of the parties to pay. The issue may be relevant in terms of custody of the children, if any, because the court will always act in the best interest of the children.
Whether the home has to be sold depends on your financial picture, whether there is anything owing on the home, who will be keeping it, and whether that party can afford to maintain it.