This law from 1907 is still on NYS' books. Researching this on the internet, apparently there have been 13 reoprted cases in the last 40 years. It does not seem that there are many convictions; most of the cases have some other criminal element to them, such as public indecency. There is a possible fine of $500 and 90 days of imprisonment.
You would go to the police to report a crime. The likleihood of it being prosecuted is very slight. There is a civil remedy for adultery - divorce.
It's one of those "never going to work" scenarios. No prosecutor will touch the case. And no, the other woman hasn't violated the law.