Getting enough votes for opening the Vaults is hard if you didn't invest in Dwarven Embassy. It's possible but trade off is that you have to make a deal with Darghelon to vote "yes" on Unpeople motion ensuring the motion to pass (you'll also need to pay 120k ProN to influence Ghenalon vote).I couldn't swing enough votes for that, I got a tie, there were two that I thought would vote in my favor but they lied! Now I'm expected to save their respective countries from the Incubus Emperor! I thought about intentionally losing to the dark seeds and letting them suffer, but I dont like losing to enemies so I guess I will have to save them.
With Dwarven Embassy funded you should have achieve success on all three motions (Unpeople fail, Orc Extermination fail and War Vaults open).