Can my car be repossessed while its parked in my yard in Virginia?

The location of the vehicle is not critical. As long as it can be seen and does not require breaking and entering, the vehicle can be repossessed.

Yes, repossessions can (and often do) occur on private property. There are limitations imposed on the recovery agents, and they know how to plan accordingly. IMO, better that car (which is actually the lien holder's, which is why it can be repossessed in the first place) be repossessed while you're at home than while you're out in public somewhere and left stranded.