I think the effects should be limited to actions that actually involve your family. I want to retain the possibility to create a character who is the younger son who hates his father and is jealous of his older brother, or any of the like. If these were implemented:
No transfer of bonds between enemies.
An inability to vassalise or pledge allegiance to enemies.
An inability to end hatred diplomatic status with another realm if it is led by an enemy.
An inability to form an alliance with another realm if it is led by an enemy.
An inability to sign treaties if they are drafted/proposed by an enemy.
An automatic premium gets added to the price of trades if you have to purchase food from an enemy.
If you lead a secret society, other guild elders aren't able to bring your enemies into the fold.
Troops recruited from a region led by your enemy will have a lower base morale due to their bitterness at having to serve their lord's enemy.
Then it would be impossible.
There are not many mechanics that involve your family, so here are a few ideas:
-Your family is unable to pledge ransom to a Judge that belongs to an enemy clan, but the ransom is lower/comes more quickly if the Judge is from a friendly family
-Investments work better in regions where the Lord is friendly/impossible if he is an enemy
-Certainly something with the family home, can't think of what at the moment.
What other mechanics uses the family?