I think that when you have kids with you, it's good to have a third adult along, if possible to help supervise the children, so that the belayer can focus entirely on her task. I realize this isn't always possible. I can easily see how this sort of accident can happen. Also, a GriGri might be a good investment for this sort of family climbing.
I might add that the belay technique taught in most gyms, the "slip-slide" method, is not the best for situations where you either can be distracted, or can't see the leader. There is a modified belay method in which the guide hand is taken off the standing part and moved down to the tail to hold the rope when the brake hand is moved in. The guide hand moves back and forth between tail and standing part and the brake hand always stays in a down position. In this way the tail of the rope is always ready to stop a fall.
I realize that you were leading, but there are times when rope needs to come in, such as when a high clip is made. Remind your girlfriend to keep her brake hand down at her side as much as possible.