@AaniK I did read your whole post and it isnt per se wrong, but thesess flaws you think I have, let me explain for you:
First we have the situation with further charging ahead. If she now charges without vigilance or anything thn yes, it would be dumb or a bad ecision. BUT she absolutely needs to confirm the position of the Threnvale Kingdom. Normally if the command comes from the king, you will get a royal seal and you NEED to show it when you make that decision, especially to the opponent, and then you declare war. Everything else is a breach of diplomatic customs, with makes you a great target for complains from other countries, what can lead at worst to a breakdown or at least really big problems of diplomatic relationships. Because no other country can know if they do it to them too. Distrust is always a case for such kingdoms, but thats why they give them their daughters for political marriage. But if you do something like that the distrust would grow too big.
Another point you mentioned is that other counries could help. To that point: they dont have a single diplomatic relationship or even trade relationship with all these countries, but with the MC coming from Threnvale and beeing from a noble family there is a point. In other words the highest chance is Threnvale. If they reject them in a normal political way it would be more than unlikely that other countries would help. Except they get something great, which they can give them to make that help worthwhile. Where they only have Greeds power, which would mean that the helping country would just use Greeds power for their own ambitions AND if things go south they can say it was all them and they got coerced.
Now we move on to the situation with putting Greed there to force the others into negotations. The moment that happens it doesnt matter in this situation, which form of deal they get out of it. For all others it would only end up that they threathened them into it. Even if they claim the point of this attack at the border, they dont have witnessess which makes it easy for Threnvale to just deny it. If they reject them at the capital (and many spys, merchants and so on will bring the happenings and information to other kingdoms), then Threnvale cant claim they never tried to negotiate peacefully.
Even if it is logical that they would just be vigilant against Greed if they do as you say, but you underestimate the fear an (in that way) active Dragon King installs within the humans. This new kingdom is an upstart which started after Greed more or less conquered it and after that he threathened Threnvale into helping etc. They would naturally assume that there is more behind the things they show in public.
This fear would rather fast unite the other countries against them beyond just mere vigilance. For example I give you youjo senki, where the empire hat a similar situation. Why did everyone band together against them? Was truly the Empire in the wrong?
But the big difference between both is something rather basic: Greeds Kingdom (again) doesnt have any relationships with other countries, which takes that approach from them, because they cant negotiate beforehand that no other countries get harmed. There are most likely enough other kingdoms who dont like (or absolutely dont trust) that Greed is forming his own Kingdom and will still see it as a form of upstart. This pride and elitism together with your approach are a really bad situation for long term political ties.
Your scenario would work for short time, but in long term it would make things worse. Because the other countries wouldnt wait several years to let Greeds Kingdom gain enough power again, but would unite and try to do something while they can. Because even if the fear a Dragonking installs is great, that would end up pushing the worries and fear of others too far, which would made them ignoring that fear and trying to do something in the militaristic way. They would prepare beforehand, but they would try. We dont even know if another Dragon King could be swayed or appear, which is another uncertainity, which only Greed could answer (and that wouldnt normally be 100% sure), but not our MC.
Now tell me where is the flaws you say they were? Militaristic power doesnt need to be used, just merely showing it off in such a way could have really bad repercussions.