I was in the same situation a couple years ago. I had always had a mild interest in skydiving, but every time I mentioned it my wife nixed the idea. My interest wasn't strong enough to make a big deal about it, so I never pushed it. I did try the tunnel in Orlando, which got me a little more interested, but still not enough to push the issue.
Then one of my buddies decided that he wanted to get a group to do tandems for his bachelor party. My wife caved to peer pressure and let me go. After seeing how much I enjoyed it, she got me a gift certificate for another tandem a year later. Not long after that, she saw a groupon for a first jump course and gave me that as a gift. She may not have realized what she was doing, but once I got through FJC, I wanted to be a skydiver.
She felt much better about it after I was able to explain the safety equipment to her. Learning about reserves, AADs, and all the emergency procedures gave both of us the confidence that skydiving was an acceptable risk. Lots of things in life have potential risk. Managing risk is a personal decision, and everyone needs to decide what their own level of acceptable risk is.
I don't have any kids, so that wasn't a factor in my decision. However, I do know a lot of skydivers who do have kids.