When I am at a stop light with my foot on the brake the car with Jerk foward then the engine turns off. It feels like something is slipping and then when I turn it back on - it's a little rough
I would lean towards your throttle position sensor acting up. I would also think that your check engine light is on. You can go to your local parts house and they might read your codes for you for free. Then get back here with your findings.