OP YANBU at all.
Three remaining members of staff decided to close early and none of them made any attempt to contact you about it.
The reason for this decision to close early seems to be that your child was the only one left and they fancied an earlier than planned start to a night in the pub under the banner of having an early Christmas Party.
The staff member you like, trust and have a private arrangement to pay to bring your daughter home if you are not there had an emergency and you seem very understanding about her reasons for leaving early and not contacting you. You had sent her a text to say you would be there by closing time to pick up your daughter anyway, so she had no need to get in touch with you or assume her colleagues would decide to pack up and leave 20 minutes before they were due to finish work, 5 minutes before you arrived in what you thought was (and what should have been) plenty of time to collect your daughter yourself.
The person who drove her home is someone who has previously upset your daughter by ridiculing her about her birthmark and who shouted at her to force her into the car and dismissed her requests for you to be contacted.
This person then wandered around your house, for reasons we do not know, perhaps to check everything was okay, perhaps to just be a nosey cow.
And she then left your daughter alone for over an hour with you none the wiser about all of this.
I think you are getting a hard time for no good reason.Your daughter is only ten and not all ten year olds are used to being left alone and they don't all know what to do for the best when the unexpected happens or cope well.
It's no wonder your daughter was upset when an adult who has previously ridiculed her has then insisted she break your very clear rules about getting into cars without your permission and dismissed her when she said you ought to be contacted.
Now maybe you should have complained earlier about this woman making nasty comments about your daughters birth mark and perhaps you could have found alternative after school care. But if your daughter is otherwise happy there and you have a good relationship with at least one other member of staff and are happy with the others then I can see why you would leave your daughter at that club, especially if the staff member you don't like isn't usually in sole charge of the children or your daughter in particular. I once had a teacher who took great pleasure in making her students blush and she would mock one boy's stammer and never failed to have him read out in class, just so she could copy him and laugh as he got more and more embarrassed and his stammer got worse. His parents complained but still kept him at the school.
And with hindsight it would have been a good idea for you to ring home when you arrived at the club and it was closed, as you would have assumed the trusted worker had gone there with your daughter, just to check that everything was okay since the club had closed early and they were gone even though you had already told her you were already on the way.
But in no way can they claim they did you, your daughter or their colleague a favour by shutting up shop early with no attempt to contact you and then shouting at a child to make her do something she didn't want to do, just so they could get an early start at the pub.