2000 Chevy Impala shakes when I STEP ON THE GAS PEDAL

HI,
WHEN I TURN A FAIRLY SHARP CORNER TO THE LEFT, I GET A SHAKE WHEN I STEP ON THE GAS.
WHEN I DON'T STEP ON THE GAS(COAST) NO
SHAKING.

WHEN I TURN TO THE RIGHT ON A CURVE, DOING
THE SAME AS ABOVE, NO SHAKING.

THIS HAS ME+MY MECH.GUESSING. THERE IS NO
COMPUTER FAULT.