At first I thought that your mom was being selfish, while I still think she is being insensitive to your dad's feelings I wouldn't go so far as to call her selfish.
She was invited to this wedding and she has every right to go. I think your dad should learn to deal with his divorce. It has been 10 years and I think he's actually the "selfish" one. Skipping his own grandchildren's birthday party JUST to avoid an inconvenient situation with his ex doesn't seem fair to you and your sisters' kids.
I know it can be hard for you to see this because HE is the one who was hurt by the divorce, and your mom is the one who wanted it but you aren't helping by allowing him to continue dwelling on the issue.
Perhaps you and you sister can have a long discussion with him and help him to see that he needs to move on. He should try to find happiness for himself and act like an adult for his kids and grandchildren's sake.
As for your mom, does she try to be cordial when she sees him? Or does she make things hard on him? If she is going to attend the wedding just make sure she knows that it hurts your dad and ask her to try to keep the PDA with the new boyfriend to a minnimum. After 8 years I would think that everyone is used to seeing them together.
Have you asked her why she insists on going? Is it because she is close to the bride or does she just feel the need to make a pointless point? If it's because she is close to the bride then there is no issue.
I hope you can all resolve this and learn to have a good time together. All the best to your dad.