Well, first the car CANNOT accelerate in this scenario - fact is IF your foot is firmly on the brake as you say, then you have about 3 times the stopping force fully applied than the engine can make at full throttle. So at least you have the laws of physics well on your side. btw, this is almost universally true with ALL cars. Unfortunately folks in the past could not relate the laws of physics with their own psychological infallibility of mind and came up with "unintended acceleration" as both a phobia AND a misnomer of fact. I hope you're NOT using your left foot for the brake and right foot still on the gas? Please don't EVER do this.So this has only happened twice, once with the 2015 Q3 loaner and once in my 2016. When the car was in Drive and I stopped for a light (with my foot firmly on the break) I felt this rhythmic "jerking" like the car either wanted to accelerate or was about to self-combust! At first, i thought is was the bass as I had my music on pretty loudly =). But when I turned the stereo off, it continued to jerk. Both cars had minimal mileage (< 400 miles) at the time. Has this happened to anyone else? Is it something I need to have checked out? Thanks in advance!
btw, only the very HIGHEST performance cars have brakes that are only close to their power, and very few race cars but dragsters have less brake power than engine power. All this means that as long as you REALLY have your foot REALLY on the brake, your engine will stall (shutoff) cuz the brakes are stronger than the engine.
Second, as for the jerkiness, if you have the brake firmly applied for at least 3-4 seconds, try just taking your foot OFF the brake and NOT on the gas and see what happens. Do this in a safe location such as an empty parking lot. This should engage your hillhold function (even on flat ground) and your car should neither creep nor roll in either direction until you apply throttle. If the vibration or jerkiness continues, yup - I'd get it checked. If it does not, you may still need to have it checked as perhaps your ABS controller has a fault and it would be coincidental that the loaner had the same issue.