...and after a couple mags the full DA function of the trigger didn't work.
Put the 9mm slide back on and see if function (with the gun unloaded) seems to be restored. The Kadet Kit itself just rides on the frame and should have almost no effect on the P-01's DA/SA trigger function -- so, unless something is catching in the Kit where the small moving insert (which is technically the "slide") moves back and forth -- the problem is most likely in the P-01 frame.
Make sure there's no JUNK in the frame after using the kit, or in the "slide" part of the kit that might be impeding movement. It could be that crap just built up in the Kit affecting smooth function.
If there's still a problem, call CZ-USA.