E.P.
Like your other post, my first thought was, it could be Leukemia but... has the doctor done any blood tests? An unusually high white blood count can indicate a concern.. or any concerns with their iron levels too. (anemia?) Do they complain of any knee/joiint pain? Are they on any kind of medicine which can cause some bruising?
Certainly doesn't sound normal and I would absolutely seek a second opinion. You don't know if it is a disease, yet, because your doctor hasn't given it a name. It could be a peculiar thing that happens to these children where there wouldn't be a cause for concern. Without further testing - you don't have all the concerns ruled out.
Good luck and please update us.