I've hunted King George County before. Wierd hunting Deer with dogs but... that's what they do there.
Have the guy (hunting the dogs) pinched. Grab a dog if you can and copy the tag info or at least a picture of the dog(s) and then find his auto. Snapshot his plate and send it to VA DEC.
They will investigate. Running dogs do NOT know boundaries but that shouldn't be your problem. the handler should have control 100% even if that's not technically possible.

My $.02