Identical twins don't run in families. Identical twins happen spontaneously. Fraternal twins however, can run in the family, but ONLY on the mother's maternal side.
It is normal for measurements to ne off ny a week or two, with this child my measurements said i was 19 weeks when i was 20, and now my uterus measures 2 weeks ahead. It is very hard to find the sex of the baby at 14 weeks, let alone 13 weeks, so maybe she meant you were farther along? It sure doesn't sound like 13 weeks. Or maybe they need a new tech, she really doesn't seem to make any sense.
Let's get one thing straight....I seriously mean that identical twins do NOT run in families! They ARE COMPLETELY SPONTANEOUS. I have had medical professionals tell me this, remember,I have identical twins, I have gone through this already, you haven't. I am not mistaken, when I was pregnant I had to go to professionals who deal with high risk patients (that includes multiple fetuses). Obviously your medical professional isn't very good if they can't even give you straight answers.
Also, I have included websites to back my claims, i have done my research and asked my doctors questions, you obviously haven't.
http://multiples.about.com/od/pregnancy/a/familytwin.htm
http://multiples.about.com/od/funfacts/a/identicaltwins.htm
http://www.thetech.org/genetics/ask.php?id=86
http://www.dadsguidetotwins.com/do-twins-run-in-families/
http://twinstwice.com/twins.html
http://www.babycenter.com/404_is-it-true-that-giving-birth-to-twins-runs-in-families_10323566.bc
Sorry sweetheart, but identical twins in your family is just coincidence, and your odds of having identical twins is the same as EVERYONE else who gets pregnant.