There are words that can be vague in certain situations. Brother-in-law is one of those words.
If a writer uses the phrase “my brother-in-law,” to whom are they referring. Is it their sister’s husband? Is it their spouse’s brother? Is it their spouse’s sister’s husband?
Sometimes the reader will know to whom the writer is referring. Other times they will not. Always make certain your own use of terminology is clear–remember the reader may not have all the information at their fingertips that you have in your head.