2006 Cadillac STS Bad cat codes p420 and p430

I have felt a shake ever since 32000 miles on this car. It happens at stop lights and while waiting in drive thru lines, dealer says it is normal with the high performance sts-v engine that I have. It's quite embarrasing when your girlfriend, who does not know anything about cars, mentions the shakes and you say it's normal that's what the dealer says. The dealership sent me away that day. After I reached 59000 miles and met a coworker who owned the same car, he tells me he has had many supercharged cars from gm from a Pontiac to the 2005 stsv and the engine never hesitated enough to shake you leg or the car for that matter. Finally a check engine light comes on and the dealer said the cat 2 (error p420) was seen. A big relief. I get a rental from the dealer and they fix the car. Part of the gold key service you get with Cadillac. The same day I get my car back, I feel the shake still. Sit idle and 95 percent of the time it's good but then it shakes until the fuel regulates back to smooth again. I went back to the dealer, the manager tells me the shake is normal with high horsepower. He plugged the gm computer into the car so I could see it showed no problems, even while it shook with the computer plugged in. Noticed a squeek in the steering wheel as I pulled in the dealership and the
manager heard that too. Again I'm told it's normal. I leave wanting to sell this car if this is what really is normal. 50 miles later the check engine light is back. I go back to the dealer, to find the same cat is bad. Then to further inspect it he wanted to pull the car in the shop to inspect if the cat ever got replaced. Comes back to tell me it is p430 this time. The other cat, which is back ordered for up to 2 weeks and it just find to drive. He can't justify a rental for me although it's the same problem as last week and I did get a rental. I'm just getting a big run around here. Questions: Is it fine to drive with a bad cat in the state of California? Does this sound like a case that should be invesigated by higher authorities? Please HELP!