People with bloodshot usually appear a tiny jagged red lines on the white of the eyes or sclea. In fact, these red lines are blood vessels. And the amount of red lines is not a good indicator. And there are many reasons that can cause that bloodshot including irritants, conjunctivitis subconjunctival hemorrhage and medical intervention etc. So, you'd better get your children an eye check by an eye doctor if you really want to know what causes the bloodshot eyes.
If your children' eyes are bloodshot, the parts that are usually white are red or pink. The eyes can be bloodshot for a variety of reasons, for example because they are tired or have drunk too much alcohol. If they are children, i think their eyes bloodshot because they get angry. They need drink enough water and have a good rest. Then they can get better soon.