I also just talked with the social worker and she asked me questions about alcohol, drugs, abuse, and my support system. When I had my first appointments at the Cleveland Clinic, I had my Mom, my hubby (Nate) and a friend of mine with me. That showed that I had a lot of support!
As for family issues, everyone has them and so did I. I was honest about it with the social worker too. I told her that my Dad left us when I was 4 years old and I had seen him for the first time in 2000 and there were some major issues. She had kind of suggested that I try to work things out with him, but that didn't make the doctors change their minds about listing me. The doctors are just making sure that you have people who support you and will be there for you in the long road ahead. You will need a lot of help after the transplant and that's a lot of what the psych eval is.....making sure that you will have it.
If you have the support, don't fret about the evaluation. If you don't have the support, then you need to get things together and get it now! Be yourself when you're there and answer all questions honestly. If you were to lie about something and they found out, then they would have reason to believe that you are hiding something and then they would be more opt to not list you. Good luck with everything and if you have anymore questions, I'm here!