Voting yes on a war implies you're the one invading.

So you can just say that the war is defensive - and send those who voted against it to fight anyway? Or how does that work in your head?

In a defensive war - there is no vote whether or not to go to war. You are immediately at war because you have been invaded.

No, that's not how invasions work. Or rather, the defense against invasions does not work that way, unless you plan to lose in about three days.

Yes it's exactly how it works. You're just looking at things from an American perspective where, owing to geography, we have a negligible chance of having to fight a defensive war. When we do get attacked eventually it's just going to be getting nuked en masse. So instead all we have is 'defensive' rhetoric for the naive. Notable the Department of 'Defense' was literally called the Department of War in more honest times.

War, real war - and not just bombing random countries with little to no anti-air defense and then huddling up in microscopic and ultra-defended zones while waving a 'victory' banner while having undisputed control over near 0% of the country, is a slow grueling, and bloody thing. This is how you end up with things like both the USSR and USA losing to Afghanistan, Russia losing to Chechnya, USA losing to Vietnam, and so on endlessly.