PC's are determined to incite a rebellion and raze a city from the inside out, how do I even go about this. (SKT)

TL;DR Party wants to create a rebellion and burn a city to the ground, what's the best way to DM this

Obligatory:
If you are Nomad the Warforged Monk, Zane the Yuan-ti Pureblood Sorcerer , Toad the Half-Orc Ranger , Felgra the Goliath Bard, or Khroh the Gnome Barbarian, don't read this.

Context:
So our wonderful party has just arrived at the "wonderful" port city of Luskan after fending off a Frost Giant siege in Bryn Shander. Arriving to the scene of large smoke billowing from the harbor, our party decided to investigate what was happening. After meeting up with the Captain of Guard and a wizard of the Arcane Brotherhood and being told that the situation was under control and they believed no extra help was needed.

The party, not taking no for an answer, insisted that they could help since they were "deputies of Bryn Shander", and after a few condescending remarks from the wizard, the barbarian decided to punch him in the face. After being apprehended by the guards, half the party tried to get the guards to release their friend under any circumstance while the other half was happy to finally have the troublemaker of the party getting in trouble. Trying to avoid an actual legal trial, the barbarian suggested that he fight, "Your most well trained combatant in a Trial by Combat"

The Barbarian lost miserably, but was not outright killed, just dragged away unconscious with the party in the dark about where he went. Due to losing a "valuable asset", the parties NE sorcerer has decided that this city must be burned to the ground and all authority in the city must die. He has made his case to the rest of the party and most have agreed to go along with it.

So my main question is, how do you DM what will essentially become trying to start a rebellion in a city, while making it fun and difficulty for the party and not just a flat out, "no I'm not letting you do this." This is currently the biggest, "we are gonna ignore what we were planning to do and all the quests we had and do this thing" that I've been thrown and have no expertise in sowing discontent or planning rebellions, so I've come here for advice.