I'm gonna call this a glitch because of how annoying it is. I've gotten Shadowmere and she follows me everywhere. Its really annoying. Every single time I fast travel she is there, ruining my ability to be stealthy. I don't want to kill her, but I definitely want some way to store her at a stable, or tell her to wait at a sanctuary.
Like I said, this doesn't seem like a glitch per se, but it's game breakingly annoying to a stealth character when their horse they cannot get rid of charges in and ruins every single encounter.