The depressed center clutches are noted for easy pedal effort and smooth action when installed correctly. Something is definitely wrong. Try starting from rest a few times in second gear. Just go easy. If the chatter is still present it is in the clutch. I doubt that it is a driveline problem. The driveline vibe will be present with the clutch fully engaged at low speed when adding power.
It is possible that the shop contaminated the clutch when installing it. The stiff action is the cable or the pressure plate, but being new, the plate is probably OK. For some reason Luk and Sachs include a rather big tube of grease with their kits to lube the input shaft. I don't use it at all. I simply clean the shaft with WD-40 on a clean towel, and then dry the shaft completely. Any grease will be thrown outwards the first time the engine is revved up and get on the disc and contaminate it. This may be what they did. Ask them about how they lubed the input shaft.
If they are willing to warranty the job that is good. The break-in period is them being slightly evasive. At the price of those components, no break-in is needed. Chattering doesn't go away. Let the shop diagnose it - all you need to say is you want a smooth clutch.