For whatever reason, Elijah, Ulysses, and Christine found themselves in Big MT.

Elijah seemed to have gone there for tech, Christine to kill Elijah, and Ulysses for... only he really knows why. Ulysses came later, and met with Elijah after Elijah met with the Think Tank, and told him about the Sierra Madre. He then managed to save Christine from Y-7 (where her skull... exploded, it seems like. SHe got better.) Elijah then worked on the collars, caused the train crash, beat the tar out of 2 of the Think Tank members, and left Big MT.

There is almost no direct activity of Ulysses in Dead Money or Honest Hearts- outside of brief mentions of him, from Christine and the Burned Man.

He then hears that the Courier lived, and invites him/her to the Divide. The Courier inadverdently set up the divide before the game starts, opening it up as a trade route and letting people in to occupy. They then take a remote detonator- either as a delivery by the NCR or a keepsake, to the Divide. Most of the nukes are triggered after the Courier left the Divide, causing Ulysses to go on his journey of self-discovery. Anyway, the "return" was, in Ulysses' eyes as best as I can gather, a metaphysical argument of the Courier's role in the world, and the world at large.