My wife and I are going to visit her brother whose kitchen is not kosher. Is it possible for my wife to cook for him using completely kosher ingredients, even if we are not going to be eating the food?

If only your brother is eating, then technically there’s a problem only if the kitchen is being used for non-kosher cooking within 24 hours of your wife’s cooking. Still you should do nothing that may create the impression that keeping a non-kosher kitchen is acceptable. If your brother-in-law is in need of assistance, buy him kosher pots and utensils.