Of course I'd let him. Who give a crap? Unless you think (or he admits) that he's been drinking, why would you care? I don't have an ego affected by something like this. It can't be humiliating, you are high mins. It's not your fault. Besides, who is going to get you in trouble? The CP is the only guy who will fire you and it's his idea.
Look, flying is not magic. It's not special. You are a heavy equipment operator. That's it. Get over yourselves.
bvll#####, plain and simple, if I am assigned PIC, then I won't relinquish that duty until we land, at the destination or otherwise. It's not about pride, or ego, it's about making sure the flight is completed safely. Can the CP land the aircraft with his high mins, and save the day? Probably, but this is about professionalism, pure and simple. Going to "relieve" the PIC of his command during the middle of a flight is unprofessional, and the PAX know it. What are the passengers going to think on this flight? Hijacking? or worse for business "that the pilot flying the airplane for the majority of the flight couldn't land the thing." If I saw a similar circumstance while riding on an airline, I would never fly that airline again. It's rediculous.
If the wx was crappier than 300, and probably 2 or 3, is this really the time to be shuffling crew arround? Whether in the hold with the auto pilot coupled up or not, that was dangerous.
That being said, maybe I could see him relieving the FO, and flying the approach as PF, and the captain being PNF, but regardless, this is rediculous.
Totally unprofessional, totally uncool.
If anyone in this scenario has to get overthemselves, its a CP who thinks that he can just barge in and take command. If he really was worried about it, he should have arranged to captain that flight, his the chief pilot, he can do that.
-Pat