Dear ,
I don't know about driving across the borders, but i know about securing storage until you sort out everything.
I moved from AbuDhabi to Dubai and used a moving company and had my furniture stored for 3 months.
There are a lot of those movers companies all over, you may google and get your desired quotation.
If want my same company, just let me know.
Good Luck, u'll love it in here ..no comparison what so ever to KSA :)
