"I don’t live with my partner so often do things without him. "
He isn't your Partner, he is a Boyfriend.
My DD's friend is desperate to have a Baby. Her partner wants their own house, get married and then go ahead with baby plans.
Your SIL/DB might have the same idea, so this is a very important step to them. It was their first Family meal in their new house, but they couldn't plan what they wanted, because you thought you should get your own way.
My youngest DD is reconsidering having a Christening because my eldest is like you. As far as she is concerned, she gets her own way, regardless.
Did she run away, because she didn't want the day completely spoilt by you arguing the toss with her?
Teens say stupid/inappropriate/self centered stuff. Sometimes it's bad enough putting up with your own, let alone two that you've never met. The dynamic completely changes. Also being Teenagers means that any relationship is going to be on their terms, you can't push things. It's best to make the meeting informal. there would have been opportunities over Summer for it to happen.
They are nowhere near being a full part of your Family and they may not want to be. You've now set things back.
As for the youngest mimicking your SIl, she hasn't got the emotional intelligence to get what really happened.