actually FSX can change weather on the fly, you just need to set the rate of change to high in the weather settings. Another way is to look into a program called FSHOST. the program is mainly used to linking FS2002, 2004 and X into 1 multiplayer server, BUT, it does allow the owner/admin to change the weather whilst the game is running. So, you'd start a MP session, have the student connect in FSX to said server. Then, with the instructor in the Remote Access webpage (internet required) you can change the weather patterns to what ever you want and send it to the server which causes the connect players sim to update immediatly with the new weather.
just google FSHOST.