It is out-dated, yes. But not everything is so black as it is tried to be presented here. A transit visa in Sanaa is no problem. Women can only enter the Kingdom accompanied by their adult male close relative, i.e. father, brother, son or husband. The visa of the country at the other side of KSA has to be in the passport and you have to hand over the vehicle documents. Count on 5 days for the visa to be issued, so plan them for Sanaa sightseeing as it would not be a wise idea to leave the city without any documents.
Even the temporarily worst things in life are good for something on a long run.
Don't dream your life. Live your dreams.