The first was the Tribunal when they became gods (made it so they were gods all along)
The second was...Talos right? Or does that count as DF?
Oh crap, forgot about the Tribunal, make that four.
1) Tribunal
2) The Marukhathi Selective when attempting to remove aspects of Auriel from Akatosh. (This even is the original Dragon Break, as it literally involved the dragon)
3) At Rimmen, when Numidium is first assembled.
4) Warp In the West
The most important part of a Dragon Break is not someone becoming a god, it is the fracturing of time (Akatosh, the Dragon God of Time). Only the King of Worm's side of the Warp involved ascension. The Marukhathi weren't trying to ascend either - their goal was to remove the elven parts of their religion. Obviously impossible, as Auriel and Akatosh are [nearly] the same. The reason the Tribunal's ascension causes a Dragon Break is not that they became gods, it is the way they became gods (using mythopoeically enchanted, earthbone bending tools on the heart of Lorkhan). On the other hand, we have the ascension of Talos, which caused no temporal confusion (that is Dragon Break). Likewise, Vivec's realization of CHIM goes unrecorded, and nothing happened when the Dwemer absorbaside-ed themselves into a god (although one could say that is because the ritual was not completed).
I'd say no, Umbra becoming a Daedric prince will not cause a Dragon break. It would depend on the second novel, of course, but at the moment it looks like Vuhumba is borrowing power. He is a powerful individual, but not technically a god.