Definitely it’s not safe after I stop the router with an M5 command and exit Mach (now I’m on the Windows desktop) to have the router starting on its own

That sounds like it is using the wrong contacts on the control relay - normally closed and using Mach to pull them open instead of normally open and using the system to pull them closed. This would cause the router to start up if mach is not running to hold the relay open.

It's wired backwards

My e stop circuit is hard wired to a master control relay not to Mach3 that controls all power to motors and relays and must be reset after Mach is running and the charge pump is receiving the signal.   The master control relay also tells Mach3 through one of the pins that the e stop has been hit so it stops also.

How it operates.
Start computer and then start mach3.  You must then press a reset button for the main control relay to close and latch in if the charge pump is receiving its signal.  
If you hit an e stop or if the charge pump looses signal (like closing mach) the relay opens and all power is removed.

very similar to a "Start-Stop Circuit"

I have never used a C33 board so I went to get some information on it.  It appears the charge pump is part of the C33 board so if it is enabled and wired correctly it should work fine. 
As Dave said it sounds like it is wired backwards.

Ray

I have the C10 and C33 BOB’s. The PC parallel cable is connected to the C33 and from the C33 I connect to the C10 with another parallel cable.

On the C10 I only have connected the 4 stepper motors and they all work fine. There is nothing connected on the pins 1, 14, 16, 17 on this board

On the C33 I have connected all Limits / Estop and they all work fine. There are no other signal pins on the C33.

On the C33 there is also the 5VDC / Enable connections which is working since the green LED is lit..

And then on the C33 there are three 120VAC connections (each connection has 3 pins for N, L, GND). One is to supply 120VAC to the board, the other is to supply 120VAC for Coolant or Vacuum which is empty because I don’t use it and the last is to supply 120VAC to the router.

When I asked the vendor how Mach3 knows that the router / coolant 120VAC outlets needs to be energized, I was told that’s done internally to the C33

So where is the wired backwards?

After many tries, it has been confirmed that the C33 is not a suitable with the C10 if you want to have the router ON/OFF functions of the C33.  To make them working together some internal circuitry must be modified in either the C10 or C33