Both my children broke the bone in their wrist, right next to their thumb (at different times). Is that a particularly easy bone to break? If so, why?

It sounds like your children broke the scaphoid bone, which is the bone at the base of the thumb side on the thumb's of the wrist. It's not very big and can be easily broken given the right conditions.

The bone is most vulnerable when the thumb is extended, as in the hitch-hiking position. A common way to break it is if you fall, most often you throw your hand out to protect your body from hitting the ground. But, as you put out your hand, your palm opens and your fingers spread out; your weight lands on the palm of your hand.

The scaphoid fracture is seen more often in active young people and certain activities, like skate boarding and roller blading, can result in such fractures. The do seem to be less common among people who use wrist guards for these types of sports.