What's this about not having the FO cat c airport qualified when going to one?
Both crewmembers need the sign in the loggbook to say they are qualified. And by qualified it means reading up on the special requirements for that airport, having seen the approach as an observer OR having flown the approaches in the sim. Both pilots need this. Being the FO and acting as an observer at the same time is not acceptable.
The FO might have been a bit touchy feely about it, but had he been properly qualified he would have been more in the loop and would've had a higher threshold for what's acceptable or not. It is most likely an experience thing, but in experience, proper training is the fundamental building blocks. I would call the training manager and discuss it...
As regards to "stop" and "go-around" there is no such thing as not following up on those calls. If I would have called a GA and this was not commenced withing 5 seconds I would have said it again. If no reaction, treat it as an incapacitation and take control if you deem it absolutely necesary. If the result of all of this is no GA and a safe landing, I'd file a report. That's how serious I think this issue is. There is no way of knowing what the reason for going around is (if it's in VMC) and there's no time to discuss it in that situation. It may screw up the days schedule if tight turnarounds are planned, but other than that, there's nothing except a few gallons of fuel to loose.
/LnS