I go a completely different route than a vehicle attached awning. I have had them in the past and they, IMO, are way too limiting for the reasons you post and more.
I have found over the years that "where your vehicle is" is not always the best place for an awning. It could be 10 feet away or a 100 feet away or even right beside your 4Runner but having a roof mounted one takes all the options away except the one right beside the vehicle. I usually just strap a 10X10 EZ Awning on the rack. I can set it up in seconds (timed it - out of the bag to full setup is less than 30 seconds) and anywhere I want it. In your case out of the reach of the dog's leash. I can use it for other occasions too, like at a beach that does not allow vehicles. Cheap, easy and versatile. The biggest reason? I can put it on either side of the 4Runner depending on where the sun is lol, including the back. My .02