Here is the way to remember root and parent
_root is an absolute reference starting at the main timeline.
ie: _root.gotoAndPlay(2) will take you to frame 2 main timeline:
takes you to frame 2 of someclip nested in the maintimeline.
You can do this for as many nested clips you have for any property or action/method or homemade functions, not just gotoAndPlay.
ie:_root.clip1.clip2.clip3.clip4.clip5._alpha=50 sets the alpha of clip5 (which is in clip4, clip4 is in clip3,clip3 is in clip2, clip2 is in clip1 and clip1 is in the main timeline) to 50%.
_parent is relative reference.
ie: if your in clip1 targeting clip2 both of which are on the same level (both in the main timeline or the same movieclip) then you would use:
(you go up out of clip1 and down into clip2)
similarily you can do this as many times as you want:
ie: _parent._parent._parent.clip2 will take you 3 levels up and into clip2
Sorry but there isn’t a _child reference just _parent
You can use either way, most people like to use relative because absolute references can be difficult to fix if you start changing your movie around. A simple analogy is to compare it to driving directions. If your discribing your neighbours address its easier to say he lives 2 houses down (possibly _parent.house2), but if your giving directions to your aunt on the other side of the country it may be easier to give the exact address (_root.city.street.housenumber)
This became a rather lengthy explaination on root and parent, I hope it is easy to understand.