You can add either, bearing in mind that if internal they will add to current loading on your PSU and you must leave enough connections for any CD device you have.
In view of your child v adult usage problem, why not spend a bit more and buy two kits of external HDs in USB cages. One for you and one for your children. The USB container is not all that expensive and you can pop any HDD of your choice inside. Also, you can use either at any one time, you don't need both at once.
Finally, if your eldest has reached an age of double figures you won't avoid the "experimental" troubles that he/she will surely cause sooner or later to the O/S which I assume you will leave on the first fixed HD!