As long as you are of age (18 or over) and have a legal right to own a firearm, you may open carry in Virginia. And since there is reciprocity between our two states, you are good to go both ways. As for carrying in the car, you can carry open or concealed (again, you have a permit), or you can carry your sidearm in a console or glove box, loaded... much like in South Carolina.
Please enjoy your stay in our state.. I visit yours twice a year.