I'm going to start this out by saying 1. I only have children under 4, so I'm lucky if I can get them to watch a decent movie without running away to find new ways to get in to something dangerous/destructive (I swear, one day I will find my one-year-old repelling down the side of the fridge). 2. I am lucky if they are listening to classical on the radio. I make the following statements as a trained musician, not from my experiences as a parent.
Have you thought about starting with operettas? Gilbert and Sullivan are, on the whole, comparable in "musicality" to the operas in the Bel Canto style, and are far more accessible (I dare you to try to claim that Turandot is anywhere close to as easy to understand as Mikado).
After that, I would suggest looking into local companies. I know of one group in my home town who does maybe a couple of operas a year. Small, volunteer organizations are far more likely to present these than large companies -- larger companies generally view that as uncouth.
I've heard some good things about opera films. I remember my dad being particularly fond of a version of Don Giovanni. That strikes me as an easy way to transition to the actual stage productions.