My guess is that "trotting" probably is not an accurate description of the locomotion. Beaver and nutria don't trot, as noted and really are not great on land runners for very far. Coatis and other carnivores do have a trot, gallop, or jog, whatever you want to call it. I bet few of us here who don't raise and show horses could actually define each of these off the tops of our heads and the terms often get used in interchanged contexts.
However, there is a rodent that might fit the description. It is herded like smaller artiodactyls, has a sort of small deer-like gait, at times, long face, rounded smaller ears, white teeth, correct coloring, rear haunch high, and about the right size and color. It is the capibara of Central and South America. They love the water. It would have to be an introduced one, such as an escaped pet or zoo animal as you are a couple thousand miles by land from the nearest sources and while they like to swim, there are no records of them crossing the Gulf via swimming.
I don't think it is likely to be a Capibara, but that is the best suggestion I could come up with from the limited description and the fact that all the other good indiginous choices were already taken.