Big red flag, I thought so when I read your OP.
You are in this girl's house, your car is on her property/in her domain. For you to argue and refuse to move your car is very defiant, and borderline aggressive. You're saying "I'm in your space, my car is here **** the rules or what you want, the car stays".
It actually got me a bit worked up reading it because I've been in this position on the other side. Girls have come to my house, any disrespect they are shown the door. Any arguing, talking back, nope, gone. My house my rules. I've had women refuse to leave, drunkenly argue with me, it's repulsive.
Yes she's a woman but she paid for that place, and invited you over, she has boundaries, for you to disregard that so you can seem uncompromising and alpha is pathetic bro and you're better than that. The fact you would argue the parking spot is crazy to me, you have no leg to stand on in that argument. If you're so defiant over a parking spot then it's pretty much your way or the highway, you need to find a doormat female you can walk all over.
I do agree with the guy above, you're taking the dominant alpha thing too far. I've been guilty of it myself in the past, being aggressive, never backing down, and being confrontational. My close friends in university checked me on it 10 years ago, over the years the anger has dissipated and I'm more controlled. You can't rule by fear, people don't respect you that way. Yes, demand respect but you also need to respect others the same way, just like the girl told you.
This needs some introspection and shadow work on yourself. Why do you feel the need to impose your will and be stubborn? I'd bet it's because you were wronged in the past and haven't let it go. I think this girl is 100% correct to kick you out. Also the dancing/flirting with other guys with me there is an instant ghost.
Good luck.