I have done some research into this, and I will answer to the best of my knowlege.
The Production Red is basically the decendent of RIR crossed with Leghorns to produce a leaner bird that lays more eggs. Although you can use them as duel purpose they are not the best choice as they don't have a lot of meat on them.
The true RIR (aka heritage) are excelent duel purpose birds that lay a good amount of eggs and have a good amount of meat on them. They are a deeper color and are bigger then the Production Red.
I can't tell you which is better with small children as I have not owned either and from what I have read, there is no temperament difference between them.