Don't know if I'm correct but I assumed the OP's bio children are older (adults) and thus not necessarily close/have lived with his step children and that he is in a position to dictate whether they attend or not.
Clarification would be useful on these points OP.
That said, it doesn't change my opinion.
If your children are adults they are free to make their own choices.
What would make a difference is if it was a child free wedding and your step children were not invited as they are children but your bio kids were adults and thus received an invitation on that basis.
However, given the comments about other family members being invited I don't believe this is the case.
It's tough because i think even if you get your brother to relent the damage has been done.
In your wife's place I wouldn't attend now even if he sent over handwritten invitations with VIP status wrapped in a bow....
So you do have to choose between your wife and brother.
She's making a stand on behalf of her children. He's being a tosser.
Which mast you pin your flag on says what sort of person you are.....