The thing is, the Dunmer see beast races as inferior, and they are VERY VERY haughty and proud AND they have 3 living Gods in the timeline. Why would they ally themselves with a race they see as slaves and inferior?
Not to seem offensive, but that would be like if the Nazi's tried to recruit Jewish people into the army when they started losing the war.
Isn't it obvious? The only reason the Dunmer would cooperate is if one of their gods told them to. Now... why would they do that, well thats really just up to the writers, but anyone with an imagination and some TES Lore knowledge could come up with something half-way plausible. The bigger problem is how do you get the other two to cooperate with the Dunmer, but its not that implausible that they would have their reasons.
Its a strenuous alliance, no doubt, but not an improbable one.
BTW, your Nazi/Jew anology doesn't work. The Jews weren't a separate power at the time, capable of existing in opposition to the Nazis. This is much closer to Russia's relationship to the Nazis and even the US later. They didn't like each other, none of them did, but at different points they were allies.