I think if you switch the order of the events around, so that the "Start of layout - Destroy ChildObj" happens before "On created - Spawn ChildObj", then it will work.
If you had lots of ChildObjs on the layout and did a "On start of layout - Destroy ChildObj", it would pick all of them and destroy all of them, which is essentially whats going on if you spawn one in one event, then destroy without specifying which ChildObj to destroy in another event. :P