If Virginia had site specific reservations, they could limit the sites people with pets can use (such as MD and PA) and charge more for those sites, $5 per day perhaps. The upcharge might discourage non-pet owners from reserving those sites, would keep all the pets in one area thereby lessening complaints, and would give the parks the added funds they need. The downside is that sites would become site specific.
An alternative would be: in the reservation system, one can book specific sized sites (>40, <40, tent). There could be a section of pet sites of various sizes, with the upcharge per site per day. This too would limit the number of sites allowing pets and confine them to a specific area but it would not force site specific reservations.