What is the relation name for my wife's sister's son's wife?
For the sake of simplicity, call her your niece. If, for some reason, you are inquired as to which side of the family she belongs, then feel free to go into detail.
So here's Bob, a married man whose wife Norma has a sister Ellen.
Ellen is Bob's sister-in-law. Cool.
Ellen's son, Phil, is Norma's and Bob's nephew; they are his aunt and uncle.
Phil gets married to Kim. Kim is Ellen's daughter-in-law, and Bob's and Norma's niece. Forget the "in-law" construct; it's clumsy.