Not to mention that the GTVA is probably much more skilled and had more fighting experience with Shivans.
Already mentioned earlier. GTVA Pilots are more skilled than UEF pilots, but the last engagement against Shivans was 18 years ago. Only very few pilots who were active back then are still on the front lines during WiH, they mostly are filling command slots or run training cadres.
However, fighting Shivans and fighting Humans are two very different things, both morally and in terms of challenge. The tactics employed differ somewhat.
Secend possibility is, that the GTVA civies learn of the war and all the unhappyness that was close to getting the GTVA government thrown down (which was only barely prevented by focussing the people on returning to Sol, if I interprete the proses correctly) will erupt back in full froce and cause the ones who initiated the attack to be driven form office and replaced with people who then sign a peace treaty with Sol.
Nope. The GTVA public is at the wrong end of a very capable propaganda machine. While most of them probably don't like the idea of having to fight a war, their government has put forth some rather convincing evidence that this war is necessary for the survival of the GTVA.
Never forget that there are literally no free communication channels from Earth to the rest of the GTVA. EVERYTHING coming through the Delta Serpentis Node is scrutinized and filtered to a degree that countries here on Earth can only dream of.