Never execute, always free them!
-> If they have good traids and stats: try to convince them to join you (if you spare them 2~3 times the sympathy should be high enough)
-> also free the ones you don't like! ...wait till they come again, fight them again until they have to take garrisons with them! ...this will make you a lot of money and it will weaken them so you have better chances to siege their castles/settlements!
...regarding the conspiracy ... try to negotiate peace! (you have better chances with high sympathy) ... if you manage to be at war with only one kingdom at a time you have so much better chances and can wipe them out one by one.
(only beeing at war with one at a time also helps you to maintain a stable income because your caravan gets attacked less often, and you have time to rebuy workshops ... just keep them spread out or in your kingdom)