Thought it was going to be a reverse because of th "nice note" but maybe not.
Has anyone said it yet? They are not second cousins! They are first cousins once removed
I reckon the cousin is like a sister to the bride.
Although, I did tell my husband I would have nothing more to do with my ILs if, after telling us that no children were invited, they invited the brides nephews (although my husband is close to his brother and sees him often) because that would be ridiculous (obviously, wedding party aside) but I accepted my kids weren't originally invited.
Shouldn't have assumed they were invited, definitely not that they're flower girls, but brother should have stated it was child free.
Your mum played a silly game, I also wonder if she would have said she wasn't paying for the third girl's dress if the other two were for your children.
Bride has done nothing wrong, although could have invited Groom's nieces. I don't think sending the invoice (stating she doesn't have to pay) to someone who offered to pay is a problem, only other way to make it clear would have been for your brother to say "you don't have to pay for their dresses, it's for Bride's cousin's children, you could always pay for x instead if you really want to contribute".