It seems like the Thalmor took advantage of the weak leadership in the Empire, and risked a two front war in Hammerfell and Cyrodiil. But the Thalmor were better organized. I think they committed their reserves in Hammerfell, but the Empire was in such disarray they didn't realize it and panicked, which allowed the Thalmor to take the Imperial City. This also allowed the Empire to retake the Imperial City. IMO Mede II bargained from a weaker point than he needed. From what I'm understanding the Thalmor also have their handsful with occupying Valenwood. However the WGC allowed the Thalmor to cause the empire to further rot from within considering the Empire cannot sneeze without permission. Nords don't take kindly to being told how to live their lives.
Tullius seems quite, shall we say corrupt, and Imperial in his thinking like he can force his will over the rest of Skyrim. Ulfric still realizes he needs to get the support of the other jarls even if at swordpoint, which face it is the way things used to be done, and still are done in this world. Remember "you're either for us, or against us." But Balguulf wants to wait to see which way the wind is blowing before he makes up his mind. He's an opportunist. He's a politician.
Whiterun has been an interesting place, being a totally neutral territory. But being neutral with non-defensible terrain (unlike Switzerland) during a civil war is not a good position. Avenicci sells armor and weapons to the imperials, true. Grey-mane sells to the Stormcloaks. Yet Whiterun is awash in used hooded Thalmor robes and Elven Armor.
Originally, Hammerfell was the Thalmor's primary target and a secondary force was sent to Cyrodiil to tie up the possibility of Imperial reinforcements. The Thalmor won their leadership position in Summerset Isle through dealing with bosmer and redguard reavers and after taking Valenwood, Hammerfell was the next logical step. Then they won a few unexpected victories in Cyrodiil and believed the Empire and its capital to be weak. Opportunistically, they switched their priorities but the Empire struck back and dealt significant blows to the Thalmor.
At the time of the WGC, the Empire was in a worse position than the Thalmor. Elsweyr, Valenwood and Summerset Isle were still firmly in their grasp, but on the other side, Hammerfell had lost a significant amount of land and Cyrodiil had been sacked. The negotiation platforms were not equal.
I don't think Tulius is corrupt at all, he's simply a soldier in a foreign land with little patience for the politics and traditions of the nords. Rikke is much more in tune with the land, for obvious reasons. Likewise, Balgruuf is anything but a politician. He's for his people and would rather be left out of the war entirely. Tulius and Ulfric forced his hand, which is something he should have expected, but that's more naivety than anything manipulative.