Upright Meaning:
When the Three of Swords turns up in a reading about family, there has often been past trauma caused by a family member or experienced with a family member. Perhaps it is now time to examine this trauma and begin to work on integrating it. I say integrate rather than heal because trauma caused by abuse in no way makes you broken or dis-eased in a way that requires healing.
Integration simply means that your trauma becomes part of who you are, but it does not define you, and it is not all that you are. In an abusive situation, the Three of Swords never asks you to reach out to an abuser to mend a relationship if you are not comfortable doing so, but there is plenty you can begin to do now to mend your relationship with yourself and begin a new chapter where you live in the realization that you were not to blame for whatever happened.
Reversed Meaning:
In a family reading, a Three of Swords reversed can indicate a reconciliation or compromise with a family member or family unit after past disagreements. Somebody from your family may reach out to you to mend your relationship, but you could still be holding on to their words or actions and unable to think about reconciliation yet. Take all the time you need, but begin the process of healing these resentments on your own before reaching out to them.