Your grammar book is oversimplifying. We use the past perfect when we are referring to an event at an earlier time than the point we are focussing on in our narrative. The choice never (or hardly ever) affects how the hearer interprets the sequence of events, but only affects how the speaker relates the events to the point in time that we are focussing on.
After her father died, she moved to her grandfather's town.
After her father died, she had moved to her grandfather's town.
are both fully grammatical, both fully idiomatic, and can both be used to refer to exactly the same series of events. The only difference is that in the second one, there is a "viewpoint" time that is before now but after her moving - perhaps the text will go on to describe events that happened at that viewpoint time.
If you are asking about using the past perfect in the after clause,
After her father had died, she moved to her grandfather's town.
After her father had died, she had moved to her grandfather's town.
are both grammatical, but I would say less usual. To me, they imply that the viewpoint in the past is in her mind, rather than a general one.