Sorry for the snarky language, but, all of these what?
It sounds like you have 3 potential train segments, divided between France and
Switzerland.
And train is not the most efficient way to go from GVA to Chamonix, so unless you
are wanting the scenic route, you actually have 2 train trips.
I would consider using the bus or shuttle (that choice depends a bit on how many
of you there are) between Geneva and Cham, leaving you with 2 train rides, unless
I am missing something in your itinerary description. For 2 individual trips (esp since
you don't say when you will go to Nice) I think you just buy 2 tickets. A pass is probably
not worth it for 2 trips.