umrah visa are being issued in doha now.. u can chk with the umrah agents...
u can drive to makkah and madina.
i drove with my wife and kids aged same as yours...
i was at the qatar saudi border at zuhr time and by maghrib, i was in riyadh. stayed in riyadh for overnight. makkah is another 1000km from riyadh.
what sort of car do u have? get it serviced/ checked up b4 u drive.