Yes the process can take 3 months then again possibly less. Are you in the states right now? If so, then just register them in school there. When you get the visas you can just transfer your children to the American School in Riyad. Just make sure you hand carry their school records with you so they can be enrolled quickly. Your husband should be able to start the process upon his arrival, which would really help.

I have been through this a few times myself. I wouldn't worry about it too much, just be patient. It is important that you bring all of their records with you though. You should notify their school that they will be leaving in the near future. Then, when it is time for you to leave they should have everything ready for you.

Best of luck.
Lisa