I read it as the girl and her mum invited your daughter to the trivia night.  No wonder they were a bit put out at you inviting yourself along.

Maybe the reaction might have been different if you had rung the mother and asked if she would mind you coming along, rather than just mentioning it to your daughter....after all, it was their outing to which they invited your daughter.

To be honest, I don't think I have many friends whose mother I would want to go on outings with.. Last time I went with a friend and her Mum to (oddly enough) a trivia night.. I was invited because her Mum thought we stood a good chance of winning if I were on the team... 

BIG MISTAKE.. Her mother is INTENSE and was really quite vocal about her disappointment when we got questions wrong