I have’t read what you’ve done so far so this is assuming you haven’t done anything: in short group everything together (lp to lp, lk to lk, rh to rh etc…) cut the power wire (5V+ DC, 3.3V+ ps) from the pads (believe it’s the red wire on ps and blue on DC but don’t quote me check out p360 thread for power wire confirmation) and splice the wire from the cord and the pad (meaning you should have two wire, one from the pad and the other from the cord ) get a switch called SPDT at radioshack. switch should have three legs. middle leg is the power wire from both pads soldered on to that. and left/right leg one for DC,PS. and that’s it.
if you get something with all buttons press and you’re using 3rd party pad, then it might be the pad because of turbo buttons or non common ground. or it might be the ps ground are not isolated. use hot glue for isolation. for best result, use first party pad.