Hmmm, I'm thinking juniper or hydrangea. Some types of juniper can get fairly tall.
There's also this sticker hedge with small stinky yellow flowers that bloom at about this time of year. I remember a corner house having it (when I was a kid in grade school), but I don't know the name. You can get native/CLUMPING bamboo as well. I've heard that the clumping variety is not as invasive as the type that spreads by runners. There's also the old standby, towering cypress. How about a privet hedge?
Do you want evergreens or non-evergreens?

If you put in something thorny the dogs will avoid it and you won't need a small fence in front of it. You could grow raspberries and get delicious fruit and keep the dogs away at the same time. Oleander grows in Florida and the deep south. I don't think you can grow it in Virginia.

Oleander probably won't survive the winter in Virginia, plus I believe it's highly poisonous to pets.

I agree about something thorny - my first thought was barberry bushes. I think you'll need something prickly to deter dogs - they can be pretty determined, and they will trample most plants to get to something they want.

I have an older dog that also loves to patrol the perimeter-make it easy on yourself & plant something 2'-3' out from the fence to hide your dog's path. I have found that my dog will go through any kind of bed to bark at someone or something outside the fence. Oleanders are not hardy in this area, but there are alot of attractive evergreen & deciduous shrubs that you can put in as kind of a 'screen'.