Well, this has been a matter of discussion and disagreement probably ever since EU2 was released (or at least since people have been working on mods).
It is certainly true that the Teutonic Order had a common administrative structure, and that the Landmeister of Livland was subject to the Hochmeister and Landmeister of Prussia (those two offices were united after 1324), however the Order always maintained Livonia and Prussia as separate entities, with different Landmeisters who often followed different policies and eventually went their separate ways. After the Second Peace of Thorn, when the Hochmeister had to pledge allegiance to the King of Poland for the Prussian territories, there was quite a clear difference between Prussia, which was part of the Kingdom of Poland, and Livonia, which was not.
Also, the political structure of the territories was quite distinct. While in Prussia, the Order ruled almost solely, in Livonia it had to share authority with the Archbishop of Riga and the Livonian cities who enjoyed a significant deal more autonomy than their Prussian counterparts. In 1419, these three parties established the Livonian diet as some kind of central authority in Livonia (look e.g. at this, which I wouldn't consider entirely authoritative - for starters, the author fails to point out at any point what kind of entity the "Livonian Confederation" was and when it was founded -, but still provides an interesting overview). So yes, there were significant political differences between Prussia and Livonia that justify separating them.
I generally think that the AGCEEP's current depiction - the Livonian Order being an independent vassal of the Teutonic Order - is quite accurate; the only real problem about this is when the Livonian Order breaks the vassalage, which really couldn't have happened so easily - but this is a problem with the representation of almost any feudal or quasi-feudal relationship in EU2.
I think one change that might be worth contemplation, however, is a cosmetic one. Calling the Prussian branch of the Teutonic Order is somewhat misleading, since the Teutonic Order was present in both Livonia and Prussia, and the current naming in a way implies the Livonian Order being something different from the Teutonic Order. As an easy solution, it might be good to rename the Teutonic Order (LAT) to "Prussian Order".
Also, as mentioned above, Livonia was not ruled solely by the Livonian branch of the Teutonic Order; there was a complicated power structure including the Order, the Archbishop of Riga, several minor bishoprics (which were usually, but not always occupied by members of the Order) and the cities, so in fact, it might be questionable whether having the country represent just the Livonian Order is really accurate.
I agree with all you say, but I think we (AGCEEP) already mentioned a name change once, IIRC it was the Prussian confederation, I supported it, but it was ruled out.
Then again.......it might have been a different game or EEP
Also, we recently changed the high % of annexation that LAT did on LIV in the early part of the game. Its now less likely for this to happen