I am probably going against the grain here, but from the clubs perspective, but at 10, your dd should be able to understand about circumstances changing, she should be able to trust that an after school club worker, albeit a different one to the usual, could actually take her home, and she should be able to rationalize this, and be able to dial a number on the phone.
I also find it hard to believe you have so little thought out regards to "the unexpected" seeing that you have such shaky after school care arrangements. Like your mobile number written down next to your phone, or something.
It is shocking that a 10 year old cant use a phone, unless she has some special needs you are not telling us about.
I am really surprised that a 10 year old would be in hysterics about a change in her routine, that she is shaking so much that she cant use a phone.
Is she usually very precious? Molly coddled?
But yes, I do agree that the club should have contacted you. I dont understand WHY they would close early, rather than wait for you to come if the arrangement was that they would only drop her home if you were not in time for pickup. It seems ODD that they opted to close early, and take her home, rather than wait for you till closing time and see if a trip home was even necessary.
From THAT perspective, your dd was right to be upset, and she was right to try and stall, but it is still a shit situation, because at her age, she shouldnt have to.
I would contact the school and ofsted about this, to be honest. Because it could appear to be a case of the worker closing the club earlier rather than wait for you, to engineer a visit to your home...