how to console a 10 year old who is all teary eyed and sulky at you being late to pick them up at school?

[Mumsfan]

l had already apologised, told her that the teacher told me it was 1555 not 1520, once back home, she slammed the door shut. l went in her room and demanded she apologise for slamming the door, she at first said l didnt apologise to her, l did, so repeated it again, sincerely, she slurs out an 'apology' with no eye contact. later l go in room to tell her some good news, she tells me to just go away. should l just let her sulk and wait for her to get over it or speak to her?

Give her not of time, and then offer a snack or drink she likes. explain it was a misunderstanding
and then talk about anything but don’t dwell on the way being late

School finish times havent changed in decades. I'd be angry too.

Tell her you should have double checked with her (or something else you think you could have done) and you're sorry for not doing that.

Apologising by making an excuse that it is someone else's fault isn't really apologising it is just blaming someone else.

You want to model taking responsibility for your actions, and reflecting on what you can do better, if you want your child to do the same rather than make excuses blaming someone else for their mistakes.

And if you want to really rub in the lesson you can tell her you're sorry for blaming the teacher and the right thing to do is reflect on what you could have done differently. And you're open to ideas on what you could have done better.

Admitting mistakes to kids is good, it means they know it is ok to make mistakes and can learn what the right thing to do is when you make them, and feeling confident they can fix things, instead of needing to be perfect and hiding or making excuses when they make a mistake.

thanks for advice all, things are fine now :)