Alright, I've completely reevaluated my estimation of Vasudan history/government and what not, and have changed enough that the original bit is more or less wrong on every level. First, let's start with some basic facts:
1. Vasuda Prime is an unpleasant place to live (even more so than I thought so before, thanks to recent discoveries)
2. There are "ambassadors" between the Emperor and the Parliament. (FS1 tech room)
3. The Imperial Dynasty is either 10,000 years old or expected to last 10,000 years.
4. The Vasudans were forced off the planet to search for "resources needed for their species’ survival" (namely water).
5. They are excellent engineers and build efficent propulsion systems.
6. Excel at "excavation and the efficient use and transport of resources."
7. "[L]ive mostly in domed, sheltered, or underground cities"
8. Government discourages mysticism and fanatical religion.
9. Vasudan language is increadibly complex.
10. There is a great deal of respect and admiration of the Emperor.
11. The Emperor has the power to dissolve an elected assembly.
Alright, that's enough. Let's get on with this mess.
The first thing we must do is make an assumption: The Vasudans are native to Vasuda Prime. They aren't the Ancients, they weren't brought there by the Ancients. There is no definitive evidence on this topic either way, so I'll make it easy on myself and say that it's not true.
Okay, from there we can set some things up. First: Vasuda Prime is a terrible place, with low reserves of water. This means that most Vasudan cities, reguarless of type, would be built on or near underground water supplies. Due to limited supplies, these cities were, until the advent of space travel, limited in size and probably fairly well scattered across the planet. Most were probably founded when one group of a city was forced to leave one city, and went off the found another.
Being spread out, and likely out of contact with each other for long periods (if not complete isolation), each city would be it's own nation, meaning the early history of the planet is dominated by small city-states, much like ancient Greece. In fact, it's very likely that until radio was invented, most of these city-states didn't have much to do with each other on a regular basis.
The Imperium and the 10,000 Year Dynasty probably appeared during this period as just another city-state of the planet. To expand, the Emperor had to project his power over the other states by some means. Thus appear the Ambassadors.
These "Ambassadors" aren't exactly what one thinks of when the word is presented. They aren't whiney, politically appointed pencil necks, but likely hardy adventurers, travelers, thinkers and perhaps even missionaries. Their goal was to go to the other city-states and encourage them to join the Imperium. Other city-state leaders probably thought the same thing and sent their own Ambassadors out amongst the world. In any case, the Ambassadors would have to very smart, as they would have to learn the complex customs and language of each city-state to get his/her message across (the large number of city-states is probably one of the reasons for the complexities of the Vasudan language). They also had to be brave and tough to actually challenge the endless deserts of Vasuda Prime.
Which means that when war came, the Ambassadors were probably put in charge of the armies. They probably continued in this capacity until the GTVA proper was set up, if they even stopped then. The wars that eventually lead to the domiation of Vasuda Prime by the Imperium were probably long affairs, that didn't end until space travel began, perhaps not even then.
The Parliament developed as a result of the Imperium's expansion. Initially, they probably only held a session for special reasons, and then were probably made up of the actual leaders of the various city-states that pledged allegiance to the Emperor, not necessarily elected officials. It would be radio that changed this, and allowed, for the first time, a permenant parliament to be called.
At this point, the Emperor and the Parliament probably began to struggle for power. Since the Emperor could now rule the entire Imperium without lower level govenors, he probably believed that they should ceade to his orders. The Parliament, now a united force, believed they should have more say. Conflict was likely, and probably never actually let up until the start of the 14 Year War.
The battles were probably fought through the Ambassadors. They took the money of the Imperium or the Parliament, and used it to wage a non-war war to gain support. It is likely that by the 2320's, the Parliament had managed to gain the upperhand in this conflict, as the Empire was under their control. (It is also likely that both Emperor and Parliament used the 14 Year War to try to gain an advantage over the other).
While the Parliament and Imperium were fighting each other in a quasi-war, they were both activily trying to eliminate various extremist religious groups. The Emperor probably did this from the start, as only he could be worshiped as a god or semi-divine, no one else. The Parliament did it to try to weaken the overall power of the Emperor, and to protect the Emperor at the same time (better to have the nut you know than the one you don't, kind of thing).
Well, that's about it. Sorry if it's a bit rambling or stops short, but I'm tired. Thoughts?