Hmmm...interesting situation. I -do- feel for you. You've accepted the parts of the issue that you did wrong and that's a good thing. Makes it easier for others to accept the things they do wrong...sometimes. =-)
At our stable, kids aren't allowed to ride horses without an adult around...period. End of story. In a perfect world, a stable should be like a little community with everyone watching out for everyone else. Now...we -all- know that this isn't the case most of the time...but it's something that should be striven for. Standing rule in the stable is that no child is left at the barn by themselves...meaning that if you are the last adult around and a child is there by themselves, you need to, at the very least, take them over to the BO's house (which is 100 yards away.) That is for the child's protection as well as the BO's and the adult's. We also have a rule that as far as volunteers and employees go, no adult is ever to be alone with a child in a non-public area.
I think that you erred in not talking to the mom directly when you decided that you couldn't take the girl home...but I also think that the mom and girl need to understand WHY that situation occurred. It wasn't as if you all of a sudden decided that you couldn't take her home. Had she been responsible and ready -on time- when you arrived or soon after, it would have been a different situation. But that's not what it was and therefore, circumstances changed. Had it been me in your situation, I would have taken the girl over to the BO's house and then had the girl call the mom and said " I am so sorry Mrs.Whatever...'A' isn't ready to go and it's going to take her an hour to properly tend to her horse. I didn't anticipate that and I really need to get home. Are there any other options to get her home after she's done?" or something to that effect.
It does sound like the mom needs a crash course in being a good "horse-rider" parent. Sometimes parents get kids into activities and have NO idea what's involved. I'm not a big fan of that because I think the parents need to have a basic idea of whats going on and what their child's responsibilities are. Their children are taking care of a living, breathing animal and you can't just toss it in it's stall and go.
Probably would be a good idea for the BO to post some policies on having kids at the stable so everyone knows how to handle the situation should it arise again.