Byzantine politics mixed with Venetian politics undermined this -- the sack of Constantinople 808 years ago was deplorable, yet was the result of a lot of mistrust, including the massacre of the Latins a few years earlier.
This was due to Venice -- Venice was part of the Byzantine Empire for a long time, so in many ways it was a war between brethren and the Venetians, smart cookies that they were, used the Franks as their weapon. Remember that even the sack was the Venetians diverting the attention of the Crusaders.
We add in the fact that the Byzantines looked down on these barbarians from the West (quite rightly, we Westerners WERE barbarians compared to the Easterners and we sent our warriors, not our civilized folks).
the disunion was due to politics -- not Frankish, dumb bricks that they were.
the problem with 1453 was that ahem, the Empire's attention was diverted to problems in the north (can't mention what exactly in a caucus thread!)
At the end of Crowley’s “1453” he quotes a description of a Mass held in St Sophia’s prior what all attendees knew was their final day before the fall of Constantinople. (I would post it but don’t have it handy). Latin and Byzantine were one for that moment. It was a beautiful story of unity in the Church. I pray for that unity.