I have one very sensitive person who makes drama over almost anything anyone says. The question she chose was, "Do you really need to cry over that, or do you need to get more information?" It has helped her get out of her little feeling circle and have the competency to look outside of her feelings and get answers that help her get along with people better.
I have another person who is sarcastic, and sometimes mean in the way she talks to others - adults as well as peers. The question she decided on was, "Before I speak ask me, is it going to be helpful, is it going to be kind, and will it make people like me more?"
I ask myself, "Is my behavior going to show who I want to be known as?" Especially when I am problem solving it is important to behave in a manner that helps solve problems, not create more because I was unwise in the use of my words.
So, why don't you give it a try? Pick a time to talk to your family and see if you can come up with some helpful questions. Consistency is what will really make a difference in how well everyone feels helped. I would love to have some feedback or some questions if you try asking a question and find it to be helpful in your relationships.