The UEF is the only legitimate authority in Sol system. They will not surrender their ships.
Sol may have been part of GTA, but the change of regime was legitimate. GTVA doesn't really have any good arguments for calling UEF illegitimate.
Of course, the GTVA has a history of
violently subduing factions that attempt to secede from the Alliance, so actually there's nothing new on that regard. Except that UEF leadership doesn't use violently xenophobic rhetorics to acquire a following.
As to why they are resisting GTVA... well, that should be obvious. They are defending their homes and their way of life. Nothing new there either. People don't like to be meddled with. GTVA comes into Sol and tries to tell them what to do, what to think, don't run, don't walk. They're in their homes and in their heads and they haven't the right. They're meddlesome.
And no, to my best knowledge the Ubuntu party did not in fact utilize Paxilon hydrochlorate on the population of Earth to gain control, or resort to any other illegitimate measures.
GTVA's best argument for the war is not that the UEF would be illegitimate regime, but their concern that the Ubuntu-ruled humanity would not be able to deal with external threats.
This argument has several problems, however. First of all it assumes that Ubuntu-grown people would not be able to adapt to do the necessary things demanded by circumstances; I should think that by the time of War in Heaven Part 1, that would have been demonstrably proven false already.
Secondly, it assumes that Ubuntu-ruled humanity would face the same external risks as GTVA-ruled humanity. This may or may not be the case; more on this further on (GTVA's assumption is that Shivans want to destroy humanity, which to me doesn't seem to be the case).
Thirdly, it presents an implied claim that the humanity under GTVA leadership would fare demonstrably and meaningfully better against the external threats - specifically, Shivans - than humanity led by Ubuntu. There is no substantial evidence to support this claim. Either faction would crumble should the Shivans really decide to put the pedal to the metal. I don't think either the Great War or Second Shivan Incursion culminating to Capella incident show that the Shivans would have true drive to destroy humanity. It seems to me rather that they have quite different interests as a whole. Obviously they have much more resources than they have used against the GTA, PVE and GTVA - why haven't they used their full might if, as postulated, they want to destroy both Vasudans and Humans?
True, the Lucifer destroyed Vasuda Prime. It tried to destroy Earth (and in the Sanctuaryverse, succeeded). But what was the ultimate consequence of Shivan activities during and after the Great War?
Before, there were two factions (humans and vasudans) that had fought a war of attrition for fifteen years or thereabouts. After a few hectic months of fighting a new threat, these factions formed a unified front which after the war resulted in the formation of Galactic Terran-Vasudan Alliance. There's no denying that most likely a huge amount of Vasudans perished in the glassing of Vasuda Prime, but how many human and vasudan lives would have been lost had the war continued?
Would the T-V war have gone on forever? Or if one faction won, what would it have meant for the other faction? Xenocide? Slavery? Integration into the surviving faction as second-class citizens (cheeky prawns)?
Similarly in Capella incident, lots of people lost their lives. But to me it seems that their deaths were not the primary objective of the Shivans, more like collateral damage. If they had wanted to invade or destroy the whole GTVA space, they could have done so. Demoralized and disarrayed, the GTVA fleets could not have matched the Juggernaut fleet of the Shivans, at least for long. Instead, they contained their Sathanas armada into the Capella system and blew it up, those maniacs.
Clearly, blowing up Capella was higher on their list of priorities than destroying humanity or vasudans for that matter.
It can be concluded that the GTVA's fear of Shivans - while for a good reason - is slightly off the mark. Shivans should be feared for what they can do and what they are willing to do to achieve their (as a whole, unknown) goals; they seem to have about as much concern for their own losses as human or vasudan losses, which is about none. However, so far they haven't in fact shown clear desire to completely eradicate all human and/or vasudan life. If they had wanted to do so, they would have done so.
Instead, they once applied a discrete amount of force against humans and vasudans, resulting in loss of Vasudan homeworld and the defeat of this Shivan task force while en route to Earth; resulting in unification of Terran and Vasudan factions and ending a long war of attrition.
As to what comes to capella incident, no one really can say for sure what their aims there were. The only certainty is that they wanted to go to Capella and blow it up, and they did, regardless of the opposition.
So, as a summary: It is a mistake to assume that shivans' goals would be so simple as to destroy humanity or vasudanity; they seem to have some agenda or agendas hidden behind their hostility. And as a final question: Why did they capture Bosch and the Iceni's command crew if their aim was to destroy humanity? Why not just... blow them up?