How do I discipline my 5 year old daughter?

She's an angel at school, and as soon as I pick her up, it's like she's a complete different child! It’s as if all her aggressions build up at school all day long, and then she takes it out on me, my husband and 7 yr old daughter. Example, yesterday she sits in the car and asks if we can go to her favorite grocery store to buy ice cream. I said no, and she had an immediate meltdown to the point where she made herself throw up. Then this morning she asks for a $1 for the vending machine at school. She knows the rule where both her and her sister get $1 every Friday for the vending machine. I don’t want her snacking on chips/cookies everyday of the week. She went into a crying fit, and said You are the worst Mommy in the world, I hate you, I hate your rules. Her 7 yr. old sister was trying to calm her down!! She’s very selfish, demanding and aggressive at home. But at school she gets along just great with her teachers, friends, and is very well behaved….What should I do?