I turned to my trusty Mammal Tracks & Signs book and learned that the Red Wolf tracks tend to look much like a large Coyote tracks. My guide shows that Red Wolves are known to be in eastern Tennessee and western North Carolina. Trying to differentiate between a wolf and a dog can be tricky. Your best bet is usually to follow the tracks to observe the behavior. Dogs are dogs and tend to leave an erratic trail. Wolves are focused and leave a trail that has purpose, usually a straight line from point A to B.
A few other points in making this determination are:
Wolf and coyote tracks will be tighter than the dogs. They tend to be more oval in the overall shape of the track and in the shape of the pads of their toes.
Wolf and coyote tracks tend to be made at an angle with the toes being deeper than the rear pad of the foot.
The claws of the wolf and coyote will be sharp and pointy. The claws of the outside toes will be closer to the centerline of the track. The dogs tend to be splayed out.
Based on your pictures, its hard to tell due to the deep mud but, my guess would be a large dog because of how the four toes are splayed out in four different directions and because the track looks so flat footed. These look a lot like my Newfies big flat footed paws in the deep snow.
Another note, the conversations about where tracks are relative to the other tracks seems to a red herring. What seems to be shown in the first picture is a direct register or an understep walk or maybe even the classic side trot of dog. Its hard to tell without seeing more of the trail but, it doesnt really matter that much because all canines use all of these walks depending on the situation.
No matter what this animal is though, its time to batten down the hatches.
Jim
