Speaking of kids - I'd type out a longer message but I've got two little ones I have to tend to at the moment - but I can say that we went through the same thing getting life insurance for my wife and ultimately had to seek out a high-risk broker.
The short story is that if you answer yes to a couple of key questions - you get your life insurance application and basically get put on a "do not insure" list. The guy we went with has contacts at insurers that he knows will write high-risk policies, lets them "informally" look over your application, and only "formally" submits your application when they've given the green light. Somehow this seems to work.
The application we had to fill out was super-detailed, and seemed like it was put together by someone who understood climbing. The downside is it's wicked expensive - we're paying ~3K a year for a 15 year $ 1 million dollar term-life policy. Anyhow - hope this helps - and isn't too depressing.
Here's a link to the guy we used:http://www.stevenkobrin.com/