Then just kill Shadowmere and forget it forever, Arvak is way cooler. And Serana is not replaceable.
Bah!
I beg to differ! "Ardvark" will never bravely charge into battle at your side, crush pesky spiders and wolves that try to sneak up behind you, or cave in the head of that troll you never saw that was about to side-swipe you.
Shadowmere is irreplaceable!Besides,
Serana is essential. Beat her down for fighting the great Shadowmere until she takes a knee, you can't kill her. When she stands up again all will be well between them

....unless of course Shadowmere won't let it go. In that case I'd suggest dismounting as far from an expected fight as possible, and if it can't be helped then fight at Shadowmere's side and kill his target as fast as possible and remain between he and Serana. This way she'll be more likely to fight you than the horse.
I should know. Serana has attacked me more than a few times. She occasionally gets mixed up in the fray and will catch a wild swing from me. Completely on accident and sometimes unavoidable of course, and I can understand her irritation...but she should know better!