Well this is interesting.
I'm on the way back from the fetch portion of A Daedra's Best Friend (hilarious quest) when I decide to nudge the main quest along a bit on the way. I swing by Riverwood and talk to Delphine, with Barbas in tow, and head to Kynesgrove to kill the dragon there. I like to travel with guys and snag ingredients on the way, so the three of us start hoofing it. On the way, we run into some Stormcloaks.
I'm Imperial, and I don't let Stormcloaks saunter on by on my watch. I start taking them out - they don't last long - and then turn to find my two companions at one another's throat. Barbas and Delphine are really going after each other. Amusingly, Barbas was winning.
Leaving them to their squabble, I and head to the dragon burial mound. After my target has emerged, we engage - I'm quite formidable now, though I still have to watch it around dragons. Part way through the fight I get tagged by an arrow. I turn around and Delphine is targeting me! And good ol' Barbas is attacking her from behind. Good dog.
I lock her in a case of ice for a while and focus on the dragon, eventually felling it. Now I've got its soul, and Delphine is still after my ass. :lol
Unfortunately, I can't talk to her and Calm isn't strong enough to chill her out. I'm going to leave her and Barbas to their little spat and hope that Delphine chills out after I take a wagon ride or two.
My speculation is that Delphine attacked me when I turned on the Stormcloaks, and since Barbas is assigned to me as a companion, he sprung to my defense. But they're both invincible, so their rivalry might never end.
If this turns out to have broken the main quest, I'll just reload from when we left Riverwood and send Barbas on his way. What a weird situation...