The GTVA's economy is pretty much in ruin most likely tying up a lot of fleet assets in anti-piracy actions. Then they also had various rebellions (again tying up ressources), the diplomatic relations with the vasudans are strained (meaning the vasudans might be unwilling to help in the police actions) and there's always the looming threat of a new Shivan incursion (again tying up ships for the reserve and patrols of their own terretory). Additionally they have to guard the jump node to Sol for the unlikely event of a UEF counterattack into GTVA terretory (Delta Serpentis is after all the seat of government and feel high command).
On top of that they have to carefully choose which personel they send into battle against Sol, to make sure they don't have any more desertions, after all half the fleet that was sent there to conquer a beachhead went over to the UEF.
So I can understand quite well why they can't simply overrun the UEF with a massed assault.
Also I think a simultanous attack on every planet in Sol wouldn't be such a good idea. Considering the superiourity of the UEF fighters, it would probably leave the GTVA capitol ships with a too thin anti-fighter screen. For me a concentrated attack on one target after the other seems to fit better with the strength and weaknesses of the GTVA fleet. Furthermore once they got Sol and Mars I doubt that the rest of the system is going to put up much resistance anymore.
Destroyers, and Chimeras and Bellerophons, are not antipirate assets. That's an Aeolus' job. The heavy combat units of the fleet are free. Governmental control is in Beta Aquilae. The trick here is to assemble a fleet with enough firepower that any attempt to stop it will require the UEF to risk being gutted. It should not be hard to do, as the UEF has very limited forces.
The UEF military has not faced a significant threat, real or pyschological, in nearly forty years. It has been inadequately funded for that time, meaning it lacks exercise experience in addition to combat experience. Its logistical depth is poor because it has lacked the means or the reason to develop it. It has no mechanism for replacing losses and few reserves. Just to top it off, it comes from a society that neither respects nor values the need for warriors.
The GTVA military has fought three major enemies in the same period, the Hammer of Light, the NTF, and the Shivans. It operates under the assumption that every new day brings with it the possiblity of Shivan-induced armageddon, and it takes that very seriously. It has been very-well funded for that reason and able to conduct regular, significant exercises. Many low-level officers and senior non-commissioned have combat experience from either the NTF or the Shivans. It's logistical base is well built up to enable commitment of all or most combat ships at any point in the GTVA, since where the Shivans will appear can never be certain. It has mechanisms in place to allow the replacement of losses or the rapid expansion of the fleet in time of war; they are effectively the same thing. And finally, it comes from a society whose warriors represent their only hope in a universe of hostility.
If the GTVA were to commit a significant proportion of its fleet assets, even a quarter, it should easily outnumber the UEF by nearly 2 to 1. It could all be over in a day, the UEF fleet or its means to continue making war crushed. It might take a couple months after that for the actual surrender, if the UEF fleet did not come out and fight to protect its logistical network, but the war would already be decided. That it's not is a political, not a military, choice.
