Arguments with mom and dad

I have arguments with my mom and dad.  I live in a crowded city where it is difficult to park.  Last week, my mom offered to drive me so that I can do what I need to. Today, she told me that she can’t drive tomorrow.  I said OK, but I still need to go.  I ask Dad to drive me and he told me NO.

Model 1
C : Dad does not want to drive me
T : He is very egoist, he has nothing to do
F : Disappointed and nervous
A : Arguments with him. Telling him that he is egoist, never wants to help.
R : Dispute with mom and Dad

I decided that I will go out by myself and figure out how to park.  I told them that.

Model 2:
C : Mom wakes up earlier to do her stuff so she can drive me without telling me
T : I did not ask her to do that
F : Nervous
A : Tell mom that she did not have to change her plan and that I can’t go by my own
R : Mom is sad and arguments

In the meantime,

Model 3:
C : Mom came to me in the morning, and says : ‘Good morning stupid girl’ and says, “it is a joke”
T : Why is she insulting me?
F : Nervous
A : Ask her, “why are you insulting me? don’t do that anymore, I am not laughing.”
R : Arguments, Mom sad

Intentional models

Model 4:
C : Mom came to me in the morning, and says : “Good morning stupid girl” and says, “it is a joke”
T : Great occasion to put boundaries for the future
F : ?
A : Tell her that she can’t insult me because I disagree with her
R : Not accepted insults in the future

Model 5:
C : Dad does not want to drive me
T : It is OK, it is his right
F : ?
A : Looking for other options to go to the city, not asking him anymore
R : Rely on myself

Any advice on the models and intentional ones?

Other question : I hate after arguments (small and irrelevant arguments), my mom and I don’t know to go back to a normal situation. Any advice?
The tension stays there.

Finally, I kind of go to the extreme in my mind. Ok, he does not want to drive me, she insulted me, I can take care of myself, not relying on them and look for my own apartment. How to avoid that?

Thank you for your answer.