Intermittent check engine light accompanied by... vibrating?!?!? (2002 Hyundai Santa Fe.)?

The car runs wonderfully 99% of the time. However, twice now, (both first thing in the morning, on cold, rainy days, if that's relevant.), I've driven about two miles and the check engine light comes on, and the car starts shaking, like someone is kicking the back of the seats with superhuman strength. There's also a rather loud "chugging" sound. As I said, this has happened twice, the first time being almost a month ago and the second being today. (I only got the car about three months ago, but I have the maintenance records from the original owner and everything looks okay.) Both times, I've pulled over, shut off the engine, then turned it back on, and everything was perfectly fine after that. What could be causing this?