Above is an image of a California rest stop. As you can see there is a sign announcing that there is a pet area and a big orange arrow pointing toward it. Immediately in the path of the direction the orange arrow is pointing is a brown and white sign informing you that no pets are allowed. It kinda makes sense in a Californian way. Just tell the dogs that Reno isn't too far away and if they can hold it you are bound to find a less confusing rest area.
Be safe out there.