The modded player home I'm working on needs one more thing, a way to get there faster than walking because it's in a very remote place, since it's not near the coasts default ships make no sense, hence I feel the situation calls for a carriage driver. Problem is, despite all of the searches I've down, the vast majority of results are about animating carriage rides instead.

Can someone please explain to me how to make a functioning carriage driver?

I haven't done it myself so I can't tell you outright how to do it. One thing you could do is to have a look at how other mods do it and learn from those. http://skyrim.nexusmods.com/mods/9544/ is probably a good mod to start with.