Minx,
I started climbing when my third kid was 2. I had always looked at the mountains and wanted to learn how to climb and finally got off my ass to do it.
Since I didn't climb before I had no kids, I can't say whether I'd climb more or less. I climb as much as I can, but that's a lot less than folks I know without kids, or with grown-up kids. Sometimes climbing pushes on being selfish. I've climbed every father's day for 4 years running, for example. I've been leaning more towards one-day trips in the past year, so I can spend 1/2 the weekend with the family. I really like doing Friday night car camps with an early start and a one day ascent. Last year I did a few this way: Mt. Saint Helens, Ingalls, Whitehorse, Silverstar, and Dragontail. But to be honest half of those were backups due to my overnight climb plans being rained out.
As for the risk factor, I err on the side of caution. I'm averse to doing very committing routes and don't see this changing anytime soon. Grade II-III is cool, but grade IV routes are probably out of the question for the foreseeable future.