"For all we know, the daughter in the letter may feel the same as my cousin did - conflicted, unsure, wanting to do the right thing but not wanting to hurt the people who raised her. The difference is in the mothers. My aunt told my cousin flat out that her father might not deserve to walk her down the aisle, but it was still the right thing to do. And inviting his wife with him was also the right thing to do. Apparently the mother in the letter is not giving that guidence."

I agree. This could be a first step to reconciliation. It's a big gesture. While it is rude to invite someone without the wife, this is a massive backing off of the "not speaking to ever again".

This is his child. He needs to go to the wedding and reception to make up for the damage he did his kids with his affair (because even adult kids are hurt terribly by the disrespect, selfishness, and obnoxity inherent in an affair). Her rudeness is less important than her major step to reconciliation.

I don't get the "angle for money" thing. If they wanted him to pay, wouldn't the bride and groom have contacted the man before sending the invitiation? After all, a lot of it must be pre-paid or paid right at the ceremony. There's no guarantee the dad will show.

The other woman here sounds likr an unreliable narrator. No acknowledgement that maybe, just maybe, the couple's behavior was disrespectful and painful to both of the betrayed spouses and the children? That maybe the couple's attitude might have something to do with the continuing animosity?