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The best solution is for your son (the groom) to put aside the past bad blood feelings for the sake of his brother. He should respect the fact that his brother is not going to cause additional strife in his own personal life by telling his girlfriend that she is not welcome at the wedding. His girlfriend would view this as her being disrespected and him not standing up for her with his own family.

Just because she comes to the wedding does not mean that they have to interact with each other. Hopefully, they can be bigger people and put aside their differences for the sake of the celebration.

I know that there are always extenuating circumstances that are not know to me, but hopefully the groom can set his feelings aside and allow his brother to be his best man and have that memory forever.