Is my wife's brother's wife my sister-in-law?

Yes, the definition of sister-in-law does include the wife of a spouse's brother. A sister-in-law could also be the wife of one's brother or the sister of one's spouse. Except in unusual cases, one's sister-in-law is not a blood relative.

The origin of the sister-in-law is late Middle English, sometime between 1400 and 1450. The two possible plural versions are sisters-in-law and sister-in-laws, although the latter is usually viewed as incorrect, even though it is occasionally seen in published works. There is also a similar term, co-sister-in-law, which can refer to the wife of one's sibling-in-law. There is also a half-sister-in-law, which is used when a person or their spouse has a half sibling.