My wife's second sister is from Canada. How can my wife prove their relationship if she wants to emigrate?

First of all, I want to remind you that your wife's second sister is not qualified to apply for your wife's immigration to Canada as a relative. Because according to Canadian immigration law, brothers and sisters are not eligible to apply. You can apply for a trip to visit relatives.

If your wife meets the requirements, she can apply for skilled immigration or investment immigration as an independent applicant. If you want to prove their relationship, you can go to the notary office to do the notarization of kinship.