But your title says Filioque. Certainly, Trinity is part of it, but to understand what caused all this, one must take into account the history, the politicis and the cultures involved in shaping the Filioque issue, and not just the Trinity.
Read this well-written summary and you will have a much better idea.
The summary you have linked to, kosta, is a very good one.
A book that both gives a detailed history of the Council of Florence from the Orthodox perspective is "The History of the Council of Florence," by Ivan N. Ostroumoff. It was written in the mid 1800's in Russia, and translated and published in England a few decades later.
It is currently most readily available in a photo-reprint of the original British publication that was published by Holy Transfiguration Monastery in 1971. Used copies can be found very inexpensively through any online booksearch engine such as www.abebooks.com and new copies be found through any number of Orthodox on-line booksellers.
There is additional material added to the HTM edition that deals with more modern issues of ecumenism, some of which I agree with, some of which I don't. But the reprint of the original core text remains an invaluable resource for anyone who wants genuinely to understand the deliberations and events that took place in Florence from an Orthodox perspective. It is not ponderous reading at all -- it is a fascinating story.
Finally, I made a typo in my post above -- it was Patriarch Jeremiah II, not Jeremiah III who wrote the answers to the Tuebingen theologians.