I'm thinking along the same lines as Soft Ride above: I don't see where someone has checked the alignment. These will do goofy wobbly things if tie rod ends are loose and less-goofy things with other worn front-end parts. Acceleration will induce toe-in (and braking will induce toe-out) leading to the tires fighting each other.

Any similar oddness while braking?

A test for this: Same road same acceleration, do the symptoms lessen noticeably when the surface is wet versus when it is dry?

It also seems like we are on the fence about whether it is some engine issue instead of a suspension issue. For this I ask: Is the wobbling/vibrating/shaking issue wobbling/vibrating/shaking at the same rate when you are going slow (like 20MPH) and fast (like 60MPH) ?

Be sure to let us know what you find . . .

Ok I'll try that. What does everyone think about getting an OEM MAF sensor from the junkyard?

You can try to get a used one, but I would not recommend that route for sensors such as the MAF, you never know what you will get, it could be fine, or it could be failing as well.
If you can get one really cheap you could try that, but I'd clean it and hope for the best.
This may help you search local salvage yards.
Car-Part.com--Used Auto Parts Market


If they want anywhere close to 80.00 I'd probably just get a new Dorman MAF, may not be as good as exact OE, but Dorman does well at making aftermarket parts.
http://www.amazon.com/Dorman-917-820...0660534&sr=8-1

I've had some luck with used MAF sensors for long-term use. Some.

Cool thing about junkyard MAF sensors, if you get it off of something that was wrecked, presumably the MAF sensor worked well enough to drive to the wreck, so it is at least good enough to use for testing. Even if it is marginal it will probably perform better than yours if yours is bad.

And no $100.00 price tag and no "no returns on electrical parts" policy to worry about.

Ok guys thank for the responses. I got a used MAF for twenty bucks from the local pull a part off a 2003 Impala( amazing how many cars are interchangeable with my regal). The good news: The CEL cleared by itself about fifty miles after replacement and I was then able to pass emissions. Bd news: Still has the front end shake on acceleration. Maybe a front end alignment is what is needed?

Yes get it in for an alignment.
Make sure the tech is aware of your shake and have him check for any play in rods ends and ball joints/wheel bearings etc.

Sounds like you had a bit of a double whammy going on, I had a similar wobble going on with my Park Ave, turned out to be the outer tie-rod ends on each side, and the tires I had were improperly balanced, that can be expected when you get Walmart TLE to balance them, never again will I go to them!

Yes I also have experienced out to lunch balancing by wallyworld.
Their machine was an antique !
Now I look for tire stores that have a modern computerized balancer with a nice LED screen!

The tire store had one of ^ these and he was how bad the Wally balance was!

Tire machine is only as good as the tech running it......also, tire machines should be checked for calibration......many aren't....

I remember my first job......they had a bubble balancer....I said, you've got to be freakin' kidding me....

Well turns out it was the inner cv joints on my passenger side. Put a new cv axle and it rides so smooth now.