THe groups will have to be in the form of movieclips. If group1 is the name of the movieclip that contains the group2 movieclip, and group2 contains the movieclip symbol, then to target that symbol from the group1 timeline you can use...
group1.group2.symbol.visible = true; // or false
Where those are instance names assigned to the objects on teh stage.
Layers are irrelevant to actionscript. They provide you with options as to how to arrange objects but cannot be affected by code, although you can rip an object out of a layer using code (addChild()) disconnects an object from its parent timeline).
The only way you woukld affcet the visibility of symbol2 if you attacked symbol1 would be if symbol2 was inside symbol1