Bearing in mind I know nothing about football.and your hypothetical is pretty woolly anyway......I have an opinion.
Is it in the normal contracts of all players that they are obliged to do PR stuff for ICT in the community if requested, or is it an optional extra they can refuse? And by extra training, do you mean the extra training "punishment" the day or so after a really poor game?
If the first is not the case, then all players are, it seems to me, at liberty to refuse participation because they are volunteers. If I were manager, I'd be noting those who volunteer to participate and adding brownie points to any decision making process as to their contract extensions so that those who are decent players. but not interested in/prepared to participate in club/local community cohesion are less likely to get contract extensions than those who do.
But I'd be much more worried about team cohesion, in your scenario, if some team members p1ssed off after the Saturday game and turned up again on Friday for the next game (particularly if they were not just permanently bench warmers)....so I'd not be allowing any employee of mine to dictate their work practices, however fantastic their abilities were....because if those abilities do not translate into playing in a system for which they have never trained to understand, and nobody else in the team have any idea where they fit into the system they have spent all week training towards implementing......what use are they really? If you could just pick good players up and throw them into a mix without any team training...why do International teams bother getting squads together to train for internationals at all?
If the first is the case, then it should be possible to organise it so the player who doesn't want to move to the area can still meet his obligations during the likes of school holidays, when his family can come up with him.(if he is Messi and you are prepared to have him dictate what he will accept). But having said that. I wonder if there is a tendency for the club to use the more popular players to the exclusion of others,,.. because, bearing in mind I can only go by what is reported in the Courier, it seems to me that, of the whole squad, relatively few are consistently reported in community activity articles...and mostly the same few.
In the second case, re extra training...nobody should be exempt.and the player who would normally be heading down the road after a game should just have to accept that he has to put his travel plans off a day or so.
But I have to admit, if it I was manager...and an prospective player said " I won't sign up unless you let me do this, that and the other" ..I 'd be advising him to find himself a team which thinks, as he does, that he is an individual more important than the team and the club.