I don't recommend attaching your dog to your ATV, if you roll or anything like that your dog will be hung up and unable to escape. The only way I'd consider attaching is with an extendable leash say 20-25' but I still don't recommend it.
Our Golden Retriever aka Box of Rocks loved to ride on our Quads. The pad in the back may help, I've seen others just attach carpet for them to lay on and dig into a bit.
In our case we had a hard box that she would ride in which kept her from moving around to much. Do put something down over the seat, once nervous their claws can dig in more then you want.