New Character Server Selection

[Garlyle]

I do know anyone could create a character on Balmung, as long as it's during a time when they aren't restricted. The same goes with making a character on another server and transferring. As long as Balmung is open at the time, they would be able to transfer.

This. Balmung is easily one of the most populated NA servers, which means it is frequently locked for new character creation. Your cousins are going to have to keep eyes open for chances to actually get into Balmung, because they're fairly rare - try every so often and they might be able to get in.

That said, there's nothing aside from that stopping them from creating/transferring onto Balmung.