You're approaching this all wrong. She's not a guy. Women don't respond to rational arguments in emotional situations.
I have a wife who is possible the most rational person you could meet at work, but when shit like this crops up, she's a fucking fruitloop.
Luckily, this fact makes them remarkably easy to outmaneuvre, if you just think a few steps ahead. Here's how I'd run it:
Call up her Grandparents, tell 'em how much you are looking forward to the reunion, and then explain the brother situation. Ask if it's OK, because you didn't want to offend them, but it would mean a lot to him.
They will (ofc) say yes. You can tell your wife then that you didn't want to upset her GPs, so you called them to check, and they insisted that see your brother.
Having done that, you've now placed your wife in an impossible situation.
She can either let you go see your brother.
Or she can carry on insisting, and have to explain to GPs why she wouldn't let you see your brother, and look like a shrew at the reunion.
Now, the important thing here is how you break this to your wife.
DO NOT FRAME IT IN AS I WAS RIGHT AND YOU WERE WRONG.
The key with women is to let them feel that they're right, whilst doing whatever the fuck you want with your life.
So you say "You know, you were right honey, I was being thoughtless about this."
(pause).
"So I called up you GPs to check that it was ok, because I really wouldn't want to upset them or your family. And they insisted that I go."
Try not to smirk when you do this as it will ruin the whole effort.