I have found that with my parents its always best to have sort of a presentation prepared. I had to convince my parents to let me rush. In my "presentation" I told them what rush would be like and the pros/cons of joining a sorority. I researched online to find out the questions that parents usually ask. Here is the link to the UK Greek parent guide. It's from 2005, but the questions and info at the end should help you with some of the problems your parents may have with joining a GLO.
http://www.uky.edu/StudentAffairs/Gr...tguide2005.pdf
You might want to see if there is something like this on your school's website that is more specific to their rules/policies.