Q: Why does my car shake when I proceed to stop?

It sounds like you have an idle speed problem. It could be a misfire that is only evident when your motor comes to an idle. This could be due to the need for a tune up or an injector problem. When you put your foot on the brake pedal, you take your foot off of the gas pedal. When this occurs, your motor returns to an idle.

There are other possible reasons this is happening, but a thorough diagnostic needs to be performed to know for sure. This will involve connecting a scanner and other equipment to determine the next diagnostic path to follow. I recommend the following to help you out; rough idling inspection which can be performed at your home or office.