Hello,
I've exactly the same problem, envoimoinshcer plugin activated and configured, it's work fine with "La poste", or any other envoimoinscher shipping method but for "Mondial Relay" and "Relais Colis", i got the same problem that arveni.
You can check any radio button to select the "Relay" when you click on submit, the same page is reloaded, and you have to do the same choice again and again...
So, no solution possible ? If i want a "Mondial Relay" or "Relais Colis" i have to programm one myself ?
Thanks