Raijin
A Mage that loves a Templar
Not to mention she was there to ensure the Empire doesn't agree to terms that breach the White-Gold Concordat again, i.e Markarth Incident.
In fact Ulfric threatening to walk due to her presence is worse than Tullius bringing her. He was almost willing to allow his countrymen to continue dying, their souls to feed Alduin and obstruct the Dragonborn from saving the world. He let personal feelings nearly get the better of him, and was willing to damn all of Nirn because of them.
Ulfric has been captured three times in his Military career. He's only won a single battle on his own, not exactly odds you want to put money on.
Under no circumstances did the Dragonborn informed Ulfric that the Thalmor will be present in the temporary truce between the Stormcloaks and the Imperials at High Hrothgar. In fact the Dragonborn wasn't even aware of this instigating act that Tullius would execute later on. It is only natural for someone to become upset, and even in rage when the other party brings an unwelcoming and uninvited third party into an important meeting that has nothing to do with the third party.
By the way Balgruuf played a huge part of allowing his countrymen to continue dying, their souls fed to Alduin in Sovngarde by obstructing the Dragonborn from saving the world when he said no to the idea of capturing a dragon in his hold, suggested by Paarthurnax. He delayed the process by wasting the Dragonborn's time by constructing a peace treaty.