Eddie, I agree with those who say to use a horizontal mesh outside the fence. I have farmed in England, Australia, Scotland and Portugal. Different predators in different countries, or diggers that do not predate, but leave holes for others that do - foxes, badgers, kangaroos (several species), dingoes (inside the dingo fence), wombats, wild pigs, stray/feral, dogs and more, including a mountain lion in Scotland!! A barb along the bottom (outside the fence posts) will stop most of them, and "foot netting" i.e. one foot high chicken mesh will stop most of the others, but I am inclined to think that wider, maybe 2 feet is needed to stop all dogs. Foot netting was enough for rabbits and kangaroos, but your idea of something heavier would be my preference too. The pigs just burst through line fences and will follow mesh until they can get around it. Not a problem for you since you are doing the whole boundary, but I had 13 miles of boundary on my Australian place, so a non-starter.
In Australia we just laid the foot netting on the ground and tied it to the bottom wire of the fence. It was soon permanently fixed by whatever grew up through it. You could put the horizontal wire inside your fence so that your vertical fence is on your boundary line, but you would have to be prepared to have coyotes still digging along the line. I doubt that the predators I have had experience of would continue digging until they were clear of the 2 feet or so of horizontal mesh, but I have no experience of coyotes. An outside barb at ground level would deter some of the digging. It stops pigs, although I have never seen a wild one the size of some of those you have in the U.S.