Traveling with a family in the winter, I would carry travel insurance. It may be part of a CC or something else, but even if it is not, it is dirt cheap on a per trip basis and takes all the hassle out of lost/delayed bags, trip interruption and other petty problems.

Traveling alone, none of this is a big deal. But, with kids between hotels & food, even an extra day on the road can be a significant expense.