not sure why you have a relay wired to a relay. all you need to do is run the RIMS SSR enable (from the PID) through both switches in series.
as long as both swtiches are on, then the RIM heater is on, if the "heat" switch or the "pump" switch or the PID control is off then heat is off.
If only the "heat" switch is off, then the pump is still on.
electrically it should work. I would add a quenching diode to the mech relay though.
****Edit. , if you are using it for pid, a high switch rate might not be good for the mech relay