Driving behaviour Cooper S

Hello, I’ve had a new Cooper S for a month and I really love him. However, from the beginning his driving behaviour seemed strange to me: 1. he starts to shiver at the rear with strong throttle. 2. With strong braking he knocks out at the rear. With a stronger braking of approx. 205 on… no idea how much, he has shuddered over both tracks on the highway. My brother and my father suspected that it was because he has so much power and is so small t and that a rear spoiler would improve something. Nevertheless, they think that this extreme behavior can not really be and I should have the settings checked at the dealer. I myself don’t have the idea of cars as you probably notice But before I embarrass myself at the dealer, I wanted to ask what you have done for experiences with your Cooper S. Is this nervous driving behavior normal?