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

Your sister-in-law is either the sister of your spouse or the wife of your brother.

If your sister-in-law is the wife of your brother, then her husband is your brother, not your brother-in-law.

If your sister-in-law is the sister of your spouse, then her husband is not related to you.

In either case her husband is your children's uncle.