Lower control arm pivot shaft woes

Your machine shop did something wrong with the installation of the bushings, and pivot shafts.
If they are properly installed, there should be no reason why the shaft should be turning in the LCA, when you try and tighten down the nut.
The shaft is quite a tight press fit into the bushing, and then the bushing itself is a very tight fit into the LCA, needing a hydraulic press to get the job done.
You sure your using regular rubber bushings, and not poly bushings?