What would the terms of the reunion have been? Why did it fall apart?
The ultimate reason it fell apart (and when the schism became really ingrained) was the success of the Ottomans, in the big picture. This is for two reasons.
First, it was politically and strategically inconvenient for the Ottoman Turks to have a united Christian religion, as it would basically guarantee an entire population of fifth columnists. Greco-Latin enmity was in their best interests, and they exploited it. '
Second, the Roman Emperor was, in the later decades of the Empire, the primary driving force behind reunification. Reunification was not only a matter of faith but it was also extremely beneficial for the Empire as, obviously, resolving differences was geopolitically expedient and would secure alliances that would potentially preserve the Empire going forward.
Theologically, the differences between the East and West were over a number of issues that Laetentur Caeli and the council addressed. These included the issue of Papal primacy, the issue of leavened vs. unleavened bread, the issue of purgatory, and the issue of the Flioque (the nature of the procession of the Holy Spirit). Laetentur Caeli was less of a compromise and basically more of a statement that these issues were discussed and states the Catholic position on all of them - namely, that the Pope has authority over the universal Church, that purgatory exists for those who die in a state of grace but with the stain of sin on their souls, and that the Filioque is a licit and legitimate part of the Creed. Laetentur Caeli does, however, provide that the use of leavened bread for the Orthodox is permissible.
The Greek bishops were either pro-union or pushed by the Emperor to accept, so they signed off on it, all save for Mark of Ephesus, who seemed to believe the filioque and purgatory were heresy and that the Pope was a schismatic. Nevertheless, the Western and Eastern Churches were mostly reunited from that point (1439) until 1453, considerable discontentment notwithstanding. Theological opposition coalesced around Mark, who died in 1444 but became an icon for resistance. Once Constantinople fell, the whole deal unraveled as the settlement was renounced by Ottoman-backed Patriarchs and bishops. It's hard to say if Varna had succeeded and the Ottomans were driven back if the deal would have held up (especially since it's unlikely the Byzantines would recover much other than being a Western-backed rump), but it's important to remember the schism was as entrenched as it was later on by this point.