But again, Iron Man's rogue gallery fucking sucks. Even Jon Favreau and Shane Black admitted that it was hard to look for good villains for Iron Man to battle, and are forced to use the Mandarin. Despite the fact that both directors criticised the character for being unrealistic and racist.
Also keeping Tony Stark alive to build a missile makes sense, since the Mandarin steals weapons from Stark Industries all the time. So it's very likely that Iron Monger worked for the Mandarin. As for Whiplash, there was suppose to be a scene in Iron Man 2 where they mention that he works for The Ten Rings. But the scene was later deleted in the final cut. So The Ten Rings is actually a worldwide organization, with the leader being yours truly, the Mandarin.