There are two ways to do this:
Method #1:
In each of the "ChildNN" tiddlers, add this line at the beginning:
<$tiddler tiddler=<<currentTab>>>
Method #2:
Create a separate tiddler (e.g., "TabsTemplate") containing
<$tiddler tiddler=<<currentTab>>>
<$transclude mode="block" />
</$tiddler>
then, in your tabs macro, write:
<$macrocall name="tabs" tabsList="Child01 Child02" template="TabsTemplate" />
In either method, the $tiddler widget sets the currentTiddler value within the ChildNN tiddler to be the currentTab name (e.g., "Child01" or "Child02"). Note that if you view a ChildNN tiddler separately (i.e., outside of the tabset), then the currentTab value is undefined, and the $tiddler widget does nothing, which is OK, since the currentTiddler value will already correctly refer to the tiddler you are viewing.
-e