During the start of the negotiations, Souma and Julius are outright hostile to each other. This causes problems and eventually after some heated exchanges between them. Julius is sent away so that the Empire alone can negotiate with the Kingdom. Once it's confirmed Julius is being "entertained" by our dear sadist maid, later on, it's found out that our sadist maid used a very potent alcohol to basically cause Julius to be so drunk that he'll be sleeping it off for a long time.
Basically, Jeanne and Souma plus bureaucrats from both sides come together to talk about the general situation of the world. Information exchanges and such. At one point, the bureaucrats are shooed out of the room for a rather serious subject, serious enough that if those bureaucrats heard it, they would be executed immediately because of the severity of the subject and the wide range of implications. There's also an explanation why Souma doesn't join the alliance, stating there's a critical pitfall in the clauses.
After this, the negotiations run fairly quickly. Souma agrees to return Van in exchange for restitution payments from Amidonia for the war. They hold things like paperwork, and the jewel broadcast thing until the payments are completed. And that the payments must be made in Imperial coinage, so Amidonia doesn't do something like making cheap coins to fake payments. Basically, the point of the restitution payments are to force Amidonia to no longer be able to support their military like they did before. In return, Souma's side will withdraw immediately and return the city. There's also a secret alliance pact between the Empire and the Kingdom to support one another against the demon lord's domain. Which entails that the Kingdom would accept requests from the Empire for military support for sending troops to support the frontline countries nearest to the Kingdom instead of the Empire.
Much later on, it's found out Souma and Hakuya had purposely wanted to use the alliance's pitfall in their favor by having the city of Van rise in rebellion against Amidonia oppression and ask the Kingdom to annex them so that the Kingdom would have a reason to invade. This was why they showed all the stuff they could do in the Kingdom, all the stuff they would be free to do under their rule. What happens instead of just Van rising in rebelling. The whole country of Amidonia goes into "coincidental rebellions" all over the place stating different reasons. This is due to a third party's meddling and the whole of Amidonia ends up being annexed to the Kingdom after threats of other countries possibly invading. Souma reluctantly ends up leading both countries as one combined Kingdom, being outsmarted by a certain little cute tanuki (Amidonia's princess).