If I sense a weakness in the royal family line, I now send the heir or other prince off on a 'special misson'. He is to lead a special 'elite' band of soldiers into incursions in enemy territory to scout ahead of the main force (which unbeknown to them never arrives). If there are any other units which are massively depleted or led by overweight cretins, they go with him. Also I hire those mercenary units which have about 3 knights in them. Then the force (usually under 150 strong/weak) are to engage the enemy and take the land for the King. It's sometimes fun to watch one or two knights in a unit take on an entire enemy force. There is no retreat - they must fight or die. Because of the sneaky nature of the mission, the King will claim the force were renegades and accept no responsibility if the force is captured and no ransom will be paid. That usually gets rid of a prince and if he somehow manages to win the battle (often neighbouring allies will join in if you send a small force) then the prince is spared.... until the next time.
I actually had a campaign where ok I was cheating a bit - picked an island faction, added a million florins, then stuck on the construction cheat and teched up the island. Then occasionally i'd send out these tiny forces of royal knights and mercenary knights into enemy territory. It's great fun when they kill about 6 times their own number before finally succumbing to the might of the enemy. Even better when they win and allies get involved. Made a change from turtling and then sending out massive armies as is the usual method when not cheating.
Anyway there is nothing wrong with weeding out the weak family members. The royal line should stay strong. Course eventually you usually still end up with an idiot if the strong one doesn't get to the throne in time or doesn't have kids. C'est la vie.
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