My initial thought is that it all seems very dramatic for a "petty" grudge, so I suspect you've only told part of the story. That said:
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You sound caught between your mother and your brother, which isn't a fair place to be. Neither your mother nor your brother should have involved you in their personal issues. If they want the best for you, they should both want you to have a healthy relationship with the other person, especially if their disagreement is over something petty. In this particular example, your mother should be encouraging you to attend your brother's wedding. If she isn't, why not?
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If your brother is the kind of person to hold petty grudges, your mother is unlikely to be the 1st person he has issues with. Is he known for holding grudges generally? If so, you are allowed to not want to be close to him.
If not, why this grudge? Who told you the details of the "petty grudge"? Have you heard both sides of the story? If you've only heard your mom's side, maybe you should talk to your brother.
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If you've decided not to go to the wedding, then at least RSVP no. There is no reason to be discourteous. Not RSVP'ing could seriously damage your own relationship with your brother and/or his future wife, which you may one day regret. No need to slam a door closed unnecessarily.
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Simply tell your colleagues you can't attend the wedding. End of sentence. You don't have to tell them why.