Shaking problem 2003 SS

I have a 2003 SS i got used with 20k miles in november of 2006. Since then i mostly used the car going back and fourth to see my girlfriend in college (Cleveland, Ohio to Tampa, Florida) so the miles are all highway, currently has 83k. I noticed at around 65k when taking a right turn the car would shake, but only when giving it gas, if i coast into a turn it rides fine. Also when accelating hard on the highway it will shake, but if i let off the gas it goes away. Also every now and then while making a hard right turn the ABS light and Trac Off light come on, and the info center will say "Service Traction System" but they go off after restarting the car. I first noticed the problem in jacksonville fl on my drive home, after getting home i took it to my mechanic, who took it to transmission specialist and pretty much told me he had no idea. 6 months later i took it to another mechanic who in turn told me "i have no idea". I have searched every auto forum on the internet and have not come up with an answer. If i can't get this figured out i'm gonna have to eat the negative equity and trade the ol' girl in. Now i have spared no expense in taking care of this car, oil has not gone more than 3,100 miles without being changed (Mobile 1 full synthetic), trans fluid has been changed every 20,000 miles, fuel filter every 5,000 miles, coolant flushed every 10,000 miles, and fuel system cleaner every oil change. The only work i've had to put into it so far is rear tie rods, stabilizer bar links, and front pads and rotors all at 55,000 miles. I think i've covered just about everything. Has anyone else had any of these problems?? and if so, how do i fix it?? Thanks in advance.

One more thing, rear defog has not worked since......well, i don't remember it ever working. Was this a common problem on the 03?

Are spark plug wires routed properly? Check at night for arcing wires. Radiation emitted by misrouted or old wires can light up MANY false codes.

this may be a bad ground...check all ground points in the engine compartment...may be also the computer grounds or computer connectors damaged/corroded etc..