If you want to get rid of a family member permanently, you can choose to throw them into the Volcano. You will receive Soul Shards as rewards for sarcrificing a Volcano, these shards can be used to improve your other Nobles. 

• Open the State Map, locate the volcano and zoom out into the County Map view. Located at the middle-left part of the Map, you will find the volcano (Lytoseau). Select which Noble(s) you want to send to a fiery death.
• If you are not in a rush, and want to help out another family, you can ask anyone if they want your unwanted Noble and have them send a proposal. Accepting a proposal adds your Noble to their family.
• You can now get rid of Baby Nobles by sending them to the Monastery. While they are in the Nursery, click a baby you need to get rid of, click the red Baby icon on the upper right. This action is irreversible and final

You can also increase the size of your family by researching ''Family Size'' through the Academy. This will let you have more family members in your Keep before you have to make room for more. 

Sacrificing a Noble while assigned to an Army will cause any attached troops to be destroyed as well. The army must be disbanded first to prevent accidentally sacrificing your troops.