I am not excusing your moms behavior...at all. I think she's very wrong.

However...(ugh) sometimes the pain of having a child break away causes strange behavior. It could be some kind of subconscious will to have you fail and always be her baby....It could be her age (hormones are, like, hellish)... it could be stuff she's going through that you don't know about.

What about going to the "library to study"? It's a message that you're working so hard you need the peace and quiet (true)...
Drive her to the grocery store and pick her up when she calls?
Explain to your dad what's going on and can she use the car?

Honestly, you both are having growing pains. The time will come when you will have to call a halt to her temper tantrums (and she's on her own with her social issues) and she will have to accept your adulthood.

But it's not easy
You will get through this, though.