So I am experiencing exactly this bug - when the player, Rikki, Talius, go into the palace of kings to confront Galvar and Ulfric.
This is from the TES wikia [Sometimes during the battle with Ulfric and Galmar, both enemies are still tagged as essential, and both of your allies just stand around after making their pre-fight speech. If this happens, you are stuck in the Palace of Kings with two unkillable enemies and two NPCs. Loading an earlier save does not prevent this from happening, and the console doesn't help either. There is no known fix for this bug.
FIX - problem can be solved via console. To make Ulfric and Galmar killable, type (without quotes): "setessential 0001414D 0" (that's for Ulfric) and "setessential 00014128 0" (for Galmar). That will make them mortal and quest will be completed.]
Unfortunately this 'fix' does NOT work. I am now looking for suggestions/help.
I really hope I can finish the Civil War quest line with this character of mine.