Clutch Or Trans?

I had a new clutch installed at a shop 3 weeks ago due to it going out and now Im having more problems with the car. From a dead stop to accelerating and switch gears it feels like I am getting a clunk or slam in the rear end on of the car. Also putting the car into first gear and letting the clutch out a little or begins to shake reàlly bad this is sitting or accelerating also, seems to becoming from around where the headers are (back of engine) I can't actually tell because the car is lowered. I had my dad put the car into reverse and had him back up into the drive way and the tires were shaking all 4.

Took it to a shop today they had told me it could be rear differential bushing or needing a new transmission. This is the same shop that had just installed the clutch so I'm iffy about trusting them.

Anyone have any suggestions?
 
What kind of clutch was installed?

Puck-type clutches (the really aggressive ones) are known to chatter on take-up. If the clutch lacks a Marcel spring or the hub is solid (or has very stiff springs) it can also chatter.

If the clutch is a full-face "street style" it could be that the flywheel wasn't resurfaced, that the surfaces were contaminated with oil, that the dowels weren't reinstalled into the flywheel etc.
 
I'm not sure what type of clutch was installed into the car all I got back was a paper with all the prices of the parts that were put into the car >.<. But if it were the tran wouldn't the car only be causing the vibrating (pulling of the car back and forth) while the car is moving rather when sitting with the brake on and putting into first gear then slowly letting the clutch out. Sorry it's really had to explain what the car is doing.
 
I heard back from the shop today and he is telling me I need a new rear differential damper which is causing the slamming in the rear end. He's also saying the part is discontinued and is trying to charge me 350 dollars for the part. Wouldn't this be the same as the bushings which only cost about 60-80? He's also still saying that the other problem which you said was clutch chatter is still my Trans. Taking it to another shop after class.
 
I heard back from the shop today and he is telling me I need a new rear differential damper which is causing the slamming in the rear end. He's also saying the part is discontinued and is trying to charge me 350 dollars for the part. Wouldn't this be the same as the bushings which only cost about 60-80? He's also still saying that the other problem which you said was clutch chatter is still my Trans. Taking it to another shop after class.

The guy's an idiot. That mass damper is not the problem. It's tuned to a much higher frequency and is there to help noise/vibration/harshness. It's Ford's effort to reduce NVH at highway speeds, when the shaft is spinning at thousands of RPM, not when you're just pulling away from a stop. As well, and as you surmise, the damper is a piece of iron mounted to the diff housing with rubber bushings. It is highly unlikely the bushings are done...

It's not the transmission but you can ask your clutch guy what could have happened to the transmission while it was on his shop floor because I take it the car was not chattering this badly before you took it in.

Definitely take the car to another shop.
 
I got under the car today and checked it out. The clutch fork is wobbling very bad when the clutch is not pressed in. As soon as the clutch is pressed down the wobbling stops. It also seems like the clutch disk or pressure plate is wobbling a tiny bit. Not sure which part I was looking at but it was painted silver. Any idea what could cause this?
 
If the clutch fork is wobbling, the input shaft is either bent, or the shaft, clutch disk or pressure plate are not lined up properly, or the flywheel is warped.

Get it fixed ASAP, if something is out of balance it can come apart with some serious force.