I am probably a poster child for "doing probabilistic thinking wrong" in some obvious way that I am blind to.

One possible mistake is assuming that problems will be independent and spread out evenly over time. That's an extreme assumption. In real life there are always more reasons for problems to cluster than to anti-cluster (so to speak), so it doesn't balance out at all. Also, problems will do more harm when clustered, because your ability to cope is reduced. So it makes sense to prepare for clustered problems. When two things go wrong, get ready for the third. That's very obvious in software engineering, if you find ten bugs, chances are you haven't found them all. But it's true in real life too.

The more general problem is that you just seem to have less life experience than your wife. To fix that, go out and get experience. Fix stuff, haggle, make arrangements... It'll improve your life in other ways as well.