Why does my bmw skip when I accelerate from a coast?

I own a 2011 bmw 328i. When I am driving
and have to hit the brakes and then try to
speed back up the car hesitates and
jumps? Also, happens when driving at high
speeds and have to slow down quickly and
try to accelerate back up. When this
happens at fast speeds the engine light
comes on. When I shut the engine off for a
few minutes and restart the car the engine
light is gone?