This same scenario JUST happened to me a few weeks ago:
My wordly aunt and I were emailing back and forth when she asked how my mom's surgery went (my dad is her brother) and I told her that I had NO IDEA my mom even had surgery!! Then I proceeded to explain (in a non-biased manner) the whole DF situation and how my folks have made the decision to shun me...she was disgusted, to say the least. It led to an open discussion about JW's and how I was treated by them, and her exact words were "No God that WE (all my aunts/uncles AND my dad) were raised to love would EVER require a parent to choose a religion over their own child!"
Apparently after that she spoke to my dad (on her own initiative) - at which her response to me AFTER the conversation was "I had no idea my brother was THIS stubborn. I would expect this from your mom but NOT my brother _ I am so sorry." The 'worldly' family never liked my mom...always thought was cooky (cause of her overly zealous JW actions) and they feel that SHE is the one pressuring my dad to shun me. She reassured me that they all (aunts/uncles) still love me and are there for me. Either way, all my aunts/uncles never cared for JWs and this situation - me being shunned and DF'd - leaves an even worse 'witness' with them. But according to my parents, TELLING my aunt about my situation brings reproach on Jehovah's name?!
I FEEL for you...cause I'm in the same situation. But isn't it amazing how clear-thinking, rational non JW human beings (family or not) can see how cruel and biased DF'ing is?