You either need to be straight honest with your dad and ask him why he thinks your mother left the way she did, or you need to tell him to call the cops on a missing person's report.
Unless your mom is on her period*10, nobody walks out over some silly little agenda.
I really don't mean to worry you or anything, and I'm sure she's fine, but what with the lack of a license, limited knowledge of the area, the fact that it's night and she COULD panic, that is all a really really bad combination.
Get off blogland
go to your dad
say that you're worried
offer to talk things out
If he's checking on you, it's either because your parents are doing this behind your back to see how you react (jumping onto the computer probably isnt the best in said case) OR he has no idea what's going on.