Car jerks violently

This has developed very recently. The car is on 74,000 miles. Whenever the battery is down to 2 points, and the vehicle is almost crawling (for example in a gridlock traffic situation, very low speed the point is), the engine will charge the battery as usual we all know this. However, if I apply the brakes while crawling now, the revs have started dipping very low. I noticed < 500 RPM on the tachometer, and the engine will make a loud sputtering noise when I let go of the brakes and it feels like the engine's about to fall out of the car. It shakes very violently, until the revs return to a more reasonable 1,200.

 

Yeah