Ah, yes, Clarksville is not far from us at all. We love log homes. My in-laws built one up in PA a few years ago, and we'd love to have one when we retire, as well.
As for the fence issue, that's a tough one. There was actually a discussion on invisible fences in another thread recently, here:
http://www.sheltieforums.com/showthread.php?t=17090
I didn't weigh in on that discussion... but I will here. I'm definitely not a fan of the invisible fences. I see them as a false sense of security. I hear too many stories of dogs escaping them, either due to the batteries in the shock collar dying, or the dog just being stubborn enough to run through the pain to get at whatever is on the other side. Even if the invisible fence does keep the pet contained, you are right, they don't keep other critters out, and if there are coyotes about, I definitely wouldn't mess around!
We do not have a fenced yard, so we exercise Lerwick on a leash in our backyard. It's certainly not too convenient, since we have to trudge out there with him every time he wants to potty, but it does mean that he's never out of our sight. We don't have to contend with coyotes here in the suburbs (not yet anyway), but there are some dogs who get loose in the neighborhood, and they aren't exactly friendly.
I guess, if it were me, I'd fence in a "potty yard" immediately off the back door (so I could just let the dog out), with sufficiently high, sufficiently sturdy fencing (as I understand it, coyotes can climb chain link fences if they aren't tall enough, so a solid privacy fence would probably be the best bet), and then maybe invest in a long 30 - 60 foot leash to let Buddy explore a bit, safely tethered to you, when you are out enjoying your lovely country yard together.