Another aspect of bribing enemy family members that hasnt been addressed yet is that they (generally speaking) make VERY VERY good governors for certain regions.
Example: You bribe a family member from Gaul, and have him govern a region in Gaul. In this instance they are one of the best choices you could make. Sending that same family member to say.....a city in Greece, isnt likely to have the same effect.
Another aspect of bribery is that it weakens the faction they originally belonged to. In this case, assassination works just as well to weaken your enemy, you just wouldnt get the additional benefit of having a new governor or general.