How do you do respond to someone who is angry, sad, or full of negative energy? It turns out that your response largely depends on the way you deal with your own negative emotions. If you tend to repress your negative emotions and deny their existence, you will most likely struggle with other people's negative emotions as well.
If you learn to acknowledge your negative emotions, if you have learned to accept them, perhaps even tried to understand them, you will be at ease to deal with people who are in a negative emotional state. You will not get pulled down by them and you will not try to stop them either. Instead, you will let them release their emotions and just be there for them. You take the negative energy in just like the ocean accepts all the rivers, polluted or clean. Before you know it, things will resolve naturally and peacefully.
Coping with emotions, being open to emotions, and even digging up repressed emotions, is not an easy thing to do, but it is something that we can learn to master. The Tao - and the world - is here to help you. See your angry bother as a reflection of something that hurts inside. And see your sad sister as a symbol of one of your own suppressed emotion. We are one. If we learn to treat people’s emotion as our own emotions, there is nothing really to do but to let the emotion express itself. Don't resist it and it will be gone before you know it.