Mute you can travel to Oman in any vehicle you like as long as your husband, brother or father are with you as you cannot cross the Saudi border unaccompanied, or without a Muharram.

You will have to own the car, I am pretty sure you cannot leave the country with a rental and you will need insurance to cross (I think you can get this at the border).

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"Diplomacy is the art of saying 'Nice doggie' until you can find a rock - Will Rogers"