What do you do when one family member wants to angrily vent to you about another family member?

I listen to them until they are finished. The least that they need is a set of ears that are willing to hear them out rather than a string if advices that's more likely to be judgemental rather than helpful

First and foremost, one should not join the cause and fight for either side. Ask the venting family member what has happened, how they feel about the situation, and why the feel angry or hurt. When they have calmed down, suggest there to be a mediation and a conflict-resolution session with the other family member. If they say no, ask them in what way they would feel more calm or better about the situation. Ask if they are able to forgive the other family member. Convince them from acting immediately. Let them know that you care about them and support them but that does not mean that you want to join their campaign.