vibration/shake 2009 trailbazer

Started with small shake and had dealer balance tires and they screwed them up and had to have 2 road force balances done on the tires. Shake is still there, more noticable at highway speeds and after driven for at least 15 minutes. Dealer said it is the tire which are Michilin cross terrains, dealer replace tire with same make and model and did not solve problem. Took to another dealer and they said it didn't shake, but by the time I got have way have it still shakes. does anybody have any ideas what this could be, could the struts or shocks been damaged by the tires being out of balance?

Shocks dampen the action of the springs, that's all they do. Shocks could be worn from tires being out of balance, but if tire balance is good, which it sounds like it is, worn shocks alone will not make it vibrate. Have you checked universal joints? The only 100% conclusive test is to remove the driveshaft(s) and check the joints for free movement, and looseness. Toe, which is a wheel alignment angle, can cause a vibration. A wheel alignment would take care of that, provided the tires don't have a wear pattern worn into them. Worn steering linkage and suspension parts can also cause a vibration.

Have had an wheel alignment done and the dealer says they checked the universals in the drive shaft , but as far as I know they have not tried to rebalance it like I have asked them to do, to eliminate the drive shaft.

Dealerships don't normally have the equipment to balance driveshafts. You'll end up going to an independent shop for that. What speed(s) is the vibe most noticeable. Drive shaft vibe is usually a "tip in" vibration, meaning it comes and goes at different road speeds. Almost always most noticeable at 35MPH and 70MPH. Above, below and between those speeds, the vibe is barely noticeable, unless something is really "out of whack". Driveshaft vibration can be heard, and or felt, (in the early stages, "sensed") usually in the seat or floor of the vehicle. Another possibility is the transmission output shaft bushing and differential pinion bearings being worn.

The shake is more when every thing in warmed up, now that it's warm out I notice it at slow speed but more noticeable at highway speed when the road is smooth, if road is a little bumpy it does hide it and if it is windy out.
Sometime I also get a clunk in the rear end of the vehicle, sometimes at stop and go, and also have had it do it when I let off gas and let the vehicle coast and step on the gas again. The dealer told me that it is backlash in the drive shafts, but sometime it happens when I am already at a complete stop and it will clunk and the truck will jerk, like the tranny is still down shifting.

That could be a dr shaft u joint, if you have that much lash in the drive train something is wrong.