Up in smoke

Question edited for clarity.
Question moved to model category.

Black Smoke is rich mixture
Blue Smoke is oil
White Smoke is Steam

What is this 'Trumbler' that you changed?? Not even Google has a clue!

Are you losing coolant? Did someone put Windshield Washer fluid into the engine oil filler? You are burning water. The ECM doesn't like it so it it shakes. At idle there isn't as much pressure to stop the water entering the combustion chamber. Likely a failed cylinder head gasket. You can do a pressure test and there is also a test that identifies exhaust gases in the coolant.

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my guess is a blown head gasket. I would do a compression test on all cylinders to be sure. these engines wont stand much high temperature running before blowing the head gasket. you can rent a compression tester from your local autoparts store usually for free.

there are a LOT of problems that could have this effect on an engine ... but from this description it sounds like your timing chain might have skipped a tooth. If your timing is off, the pistons will not fire at the correct time, and will cause a violent shake in the engine, and the engine will lose almost all power. This issue would also cause a hard start whenever you try to get your car started, so it may not be this ...
You might have a leak in your head gasket which is leaking either water or antifreeze into one of your pistons. When you start the car, is there a sweet smell in the exhaust? If antifreeze gets into a piston, it usually stops that piston from firing at all. This could cause a violent shake in the engine, and might not cause a hard start, so it would only be noticed when you start driving.
You could have a dead spot in your distributor cap -- the piece of the engine that distributes electrical charge to the spark plugs. Replacing the plugs is a first step to finding out if it is this problem -- it is cheaper and easier to do than replacing / repairing the distributor cap. When the plugs don't want to fire correctly, it has the same effect on the engine as antifreeze in your engine -- a violent shake and diminished power.
There is a SMALL possibility that it could be your transmission. If your transmission is getting stuck in the wrong gear, or between gears, the engine will try to pour out power, but will get so bogged down by the malfunctioning transmission that the whole car will shake. This is a VERY rare problem, but it does occasionally happen.
Your car's computer might not be sending or receiving the correct information to or from the engine. If this is the case, it could be pumping a different amount of fuel to each cylinder, causing the engine to fire too hard sometimes, and too soft other times. This would prevent you from getting proper acceleration, and could cause a shake in the car, but I don't think it would be a Violent shake like you described.
You could have a bent Cam, which would not allow the valves to function correctly (but this would probably keep the car from starting). It could be a bad bearing in the engine (but this would probably keep the car from starting at all). You could have faulty valves (but once again, it would probably not start at all). There are a lot of other possibilities as well ... but I think you get the point here. It is going to take a while to figure out exactly what is wrong. If you have a friend who is willing to help you out, or a really cheap mechanic that you can take it to, you'll probably save a lot of money over taking it to a corporate shop. Best of luck!

You have antifreeze leaking into the cylinders....and when the spark ignites the fuel in the cylinder, the antifreeze is in there also giving you the smoke....

What does all this mean?

More than likely, you have a blown head gasket.....or a cracked cylinder head.

Yes, the head gasket may have broken or the heads aren't mating properly with the block. At any rate, the leak is probably from the cooling system to the cylinders of the engine.

YOU SAW SMOKE COMING OUT EXHAUST PIPE.SOUND LIKE BLOWN HEAD GASKET.TOO MUCH ANTIFREEZE GOT IN THE CRANKCASE AND CYLINDER BLOCK BY THE PISTONS CAUSING ENGINE TO HYDROLOCK.CHECK CRANK CASE TO SEE ITS FULL OF COOLANNT.IT WILL LOOK LIKE A MILK SHAKE.

Black smoke means buring rich. Have the vehicle's ECU scanned for codes and do the repair the codes describe. I'm gonna take a stab in the dark and say Mass Air Flow Sensor.(MAF)

Do you know where the antifreeze went that left the coolant system. Is there a leak you can see on the ground where you park? Is it burning it through the engine? If so you might have antifreeze building up in the cylinders and that will cause your car to run rough. When it does run, do you have white smoke coming out the exhaust? Does it smell like antifreeze? Let me know

It could be 3 things: Temp sensor, thermostat, or fan relay. Fans don't usually turn on until car has been idleing for a while. I first would change thermostat, then relay, then temp sensor. Coolant must be 50/50 mixture for water pump to have proper lubricant from antifreezer. Do not go any further than a 60water/40antifreeze mix

The key to this is likely the belt. Is the belt there? Is the tension correct? If OK, do all the drive and driven pulleys turn when it is running? Did it overheat again on the trip back home? Check the system for leaks. Even if you find the problem was not the thermostat, change it. Do not change the pump unless it has a leak or other mechanical failure. Like a bad shaft bearing.