Dear Aunt,
Your sister-in-law definitely appears to be a name-stealer! I can completely understand why you would be mad as hell. (And BTW, I personally like your version and spelling of the name better.)
But should you apologize? Well, you have a right to be angry. You don't ever have to apologize for how you feel, but sometimes we might need to apologize for what we do. It seems like they shut you out not because of the same-name situation – which you were willing to let go – but because of that fight your husband had with his brother. And if they “had words,” there's a good chance your husband said something for which he might want to apologize (i.e. name calling, insults, etc.). I agree that avoiding family functions is childish, but Mr. and Mrs. Namestealer may have their own valid reason for being angry.
Does this mean that they were right to steal the name? Of course not. Should your brother and sister-in-law apologize too? Yes. But it really seems like you two might be the more mature adults in this situation! Your husband (or the two of you) might want to say something like:
“As you know, I was really upset and hurt that you chose a name for your daughter so similar to the one we had picked. Because I was hurt, I said some things I shouldn't have, and for that, I'm sorry. We'd really like to move forward with our family life and be a part of one another's lives again. Would you give us that chance?”
I think your instinct to let it go was correct. I know family members can do terrible things that warrant being cut out of one's life, but this is not one of those things. Keep the big picture in mind and consider your priorities. Do you want your son to grow up never knowing his cousin, aunt and uncle? Are you going to let pride and "being right" get in the way of family? It's really not worth it.
And just think – if you patch things up, one day you can tell your niece YOU picked out her name!
Humbly yours,
Issuesgirl