Because you have the charge pump disabled on the PMDX-126, the outputs from the PMDX-126 *MAY* turn on and off while the SmoothStepper powers up and configures. I say "may" because I don't know what happens to the SS "parallel port" pins while the SS is starting up and while the Mach3/Mach4 plug-in is initializing the board. But the 126 will do whatever the SS tells it to do.
There should be no connection between what happens on the pin 16 or pin 17 outputs and pin 1 driving the relay. At least not in the 126.
Are you powering the SS from the 126 or from a separate power supply?
Are you running Mach3 or Mach4? If it is Mach3, double and triple check that you don't have multiple Mach signals driving pin 1. Check the motor step/dir pins as well as the output signals. Does the SS still have its own pin mapping config dialog? If so, look there as well. Or post your XML file. I'm pretty sure Mach4 won't allow multiple signals to be mapped to the same output pin.
When you say "sometimes the relay'router is always on", is that after everything is up and running? Or is that during startup?
Does the K1 relay behave differently if you disable the motor axis driving pins 16 and 17?