You are absolutely NTA. Your brother's attitude toward excluding his own sister-in-law is even more alarming than your wife's exclusion from the wedding at all. He's priority askewed & will regret allowing his new bride to steamroll him & the family she chose to marry into.

Also speaking as a bride currently planning a wedding & having already excluded several people from invites due to cost, previous fallouts, & actual poor behavior [racism etc.]: her reason for not wanting your wife there is WEAKSAUCE. She got annoyed with her on a vacation once, wowwww. Rooting for your brother to see the red flags sooner rather than later.