There is no question about it, the Captain is the commander and will decide on the relevant course of action. That is his(her) legal and absolute responsibility and what the company pays him for. As such the final decision will rest with him as to how he wants the flight conducting. It might well be (and often is) that the First officer will fly the aircraft in the role of PF for emergency situations that arise whilst that role is being executed. It is often desirable and preferable that is the case. It should have been briefed prior to departure who will do what. Obviously if the commander deems it fit to change the roles at a point in time for whatever reason, then that is his decision, his responsibility and of course his right.
Unless there are overriding considerations you should carry on operating in the role and in accordance with both the standard and emergency operating procedures as briefed. Until there is an instruction to change roles, don't!
This business about whose leg it is, is an administrative requirement. The allocation of PF and PNF sectors may well follow a standard format or procedure, but they are subject to the captains authority and final decision at all times.