No, she just objects to being at the same table with Ulfric. It's an understandable personal reaction and similar to Ulfric's reaction at Elenwen being there. It has nothing to do with policy, and she backs down immediately when Tullius pats her on the head and tells her to shut up.
Please, Elisif's own household and everyone in Solitude knows that Elisif is just a figurehead. She expresses no opinions on anything of substance. She's not completely spineless, because it takes some guts to stay in Skyrim after what happened to Torygg, but basically her chair is just empty.
I have to say, I agree completely. Elisef is young and inexperianced, and yes a little bit foolish if only because of those two things, and is being used as a puppet. Thats not to say she could not grow into the role, but it certainly isn't happening while Tullius has her by the ponytail.
Really, the more I play the game, the more I find it easier to overlook Ulfric and the Stromcloaks faults. Initially I supported the Empire because of nostalga and the 'unified front' theory. Then I was sitting on the fence. Now, i'm really seeing an independant Skyrim, allied with Hammerfell and the remaining Emipire forces as standing a better chance - and not having so much corruption on the home front either. Plus, despite having a semi-famous VO, Tullius doesn't hold a candle to Ulfric in sheer charisma, interesting characterization, and depth.