This is how I see the events of the past 28 or so hours:
She persuaded you to go to the shop with her because she wanted something. You bought her what she wanted, carried it home and tripped and fell carrying her shopping. She stood there and screamed at you.
Fuck all consequences.
A man was so appalled that she left her mother lying in the street he got out of his car to help you. He - a total stranger - stopped what he was doing. She made you pick up the bags of her shopping you were carrying.
Fuck all consequences.
When you became upset she screamed at you again and walked home and left you, injured, carrying her shopping.
Fuck all consequences.
Then she called her dad and lied. She told you that she was angry that you weren't giving her a lift and bullied her little brother into carrying her bags. And went off for a lovely sleepover with her friend.
Fuck all consequences.
Today she has stayed all day having a lovely time with her friend and found out when you're collecting her little brother from town so she can swan in and get you to take her home too.
Fuck all consequences.
Have you ever punished her? You sound like you're really grateful for her talking to you at all. But she's absolutely horrible to you and you let her.
If she is perfectly lovely to her friends, achieving brilliantly at school, her behaviour is a choice. She gets a kick out of being a cunt to her mother. It's fun, it's a power trip. She's a bully. I bet she bullies kids at school too. But not overtly, subtly.
I would have the I love you but don't like you conversation. I would tell her you're disappointed and ashamed.
Her behaviour did not just affect you, the man who stopped to pick you up saw this nice middle class girl leaving her mother lying on the floor. He could be her next potential boss.
You need to come down hard on her.