There is a function of the IIRC GameDef that allows to translate a path string that uses the "$home" or "$user" (e.g. "$user/missions/test/bla.mis") variables into the system path (e.g. "C:\\users\\...\\missions\\test\\bla.mis"). The "$home" variable points to the game install directory.
Not sure if you can access this function from the AMission context. Try this to get to GameDef
Code:
if (GamePlay is GameDef)
{
GameDef game = (GameDef)GamePlay;
gameServer. ...;
}