Sorry for the belated response but i recently bought a red 93 Sunbird and have done some research (after overpaying for the car). You might want to get it towed to a Pontiac Dealership or the dealership which sold you the car once you finish looking at
www.nhtsa.dot.gov. In summary there is a "VEHICLE SPEED CONTROL" recall which could be the lack of acceleration. I have similar shaking (but i wouldnt describe it as "violent") at 55 mph and 75 mph but that could be due to my alignment. And it appears that I too have below normal gas milage partly due to maybe the recall. Another simple help would be to check the air filter since "a clogged air filter alone can cause up to a 10 percent increase in fuel consumption" (Consumer Reports). Oh and with your mechanic problem, i suggest that you look at some automotive laws to get some of your money back since the repeated visits obviously did not fix your problem. A problem that is THEIR JOB to fix. Next advise, please just take one day to try to find a respectable mechanic, one that has updated certifications (make sure it is AAA-aproved in
www.aaa.com along with the your local Better Business Bureau for complaints) and shop around for their estimate prices (there are a lot of unecessary things that the mechanics charge that would not alleviate your problem) making sure they stick to the manufacturer’s recommended services. Whew, hope that can help you out even just a little bit.
Good Luck.