Have armies fought alongside private contractors throughout history?

Yes there have always been non-military combatants in wars. Mercenaries were hired frequently during the Middle Ages by various armies to fight their battles. Later it was common practice to use "privateers", privately owned warships, to attack the shipping of rival sea powers without actually going to war.

The East India Company had its own private army, which it used to further its commercial and political interests in the subcontinent. More recently, private contracted fighters have been used in most major conflicts in Africa. How will US officials function in Iraq in the short term while their contractors are banned? American diplomats depend on Blackwater for their security, so for the time being I suspect that they will continue to provide that protection until an alternative arrangement can be reached.

Both sides have agreed to wait for the results of the investigation into the shooting before taking further action. Would the Coalition have to draft in more troops if private ... more.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.