Yea, the aggressor would have to start out with a sizable army near your borders (as in occupying a city that is near your borders) before the AI would want to start bullying around a player. Similarly, when a player bullies the AI, the AI would look at potential allies (diplomatic situation) as well as its own overall military power vs their perception of your military power.
This second event could be aided by bringing a sizable force within an area you KNOW is within their LOS 
Additionally, NSNs (Non-Sovereign Nations) could be impressed (might culture) or diplomatically made to be your vassal. This would give you less control than outright capturing the city, however you would have approx 90% diplomatic influence over the nation as long as it remains your vassal, and this would remain the case until the Vassal's mortal leader dies and is replaced with a less-than-loyal heir.
Now, if the mortal leader's heir is not entangled by foreign politics, it will remain your vassal. If their heir is directly part of your family line, you gain the city. If the heir is entangled with another player, the city becomes vassal of the other player. If the heir is directly part of another player's family line, then the city joins the other player. If the heir is rebellious or in other ways disloyal then the Vassalage will rebel and become an independent city. Any armies/soldiers contructed by the Vassal city are controlled by the politics of the Vassal Nation. I have been talking as if Vassals are only one city, but really its a 3rd party nation controlled by a Champion. It could have multiple cities.
A city will never simply "break away" from a nation (unless "culturally impressed"). I suppose there could be certain events where a city stages a rebellion, however for the most part your cities are your cities. Vassals can switch allegiances, and have the potential to be consumed by Sovereign controlled Nations, however Sovereign Nations can not vassalize each other.
However, if a Sovereign dies the cities don't simply disappear. The cities become independents, ready to be either conquered or vassalized. Also, if two nations are very closely connected with family ties ... if one Sovereign dies the other Sovereign will likely get most or all of his cities.