Only allowed to travel to connecting airport

This is a very strange situation (for me at least). My father has a return flight from A to B (both outside the Schengen area) with connection in Rome (Fiumicino). The flight from Rome to B is handled by a different airline but everything is a single reservation.

At the check-in desk in A he is informed that he needs the yellow fever vaccine certification in order to enter B. Since he doesn't have it, the airline allows him to travel to Rome only (he has all the required documents to enter the Schengen area). In Rome he will have to pick up his luggage and try to check-in with the other airline to see if they will accept him. It's worth noting that I know several people that have done the exact same route in the past few months (and I have also been in B myself several times) without problems, so unless this regulation is extremely new I'm sure he will be allowed entry in B.

Now I have many questions:

Are you actually able to check-in during a connection? Remember it's all a single reservation.
If the airline won't check him in, can he change the flight during the connection to a neighboring country of B?
If the airline won't check him in and the change is not possible, will he be able to use the return flights?

I guess I will have answers to all this very soon, but I wanted to see if anyone has experienced something like this. It is certainly the first time I come across this.

Thanks!