"Hierdoor luistert ze niet."
Translation:Because of this she does not listen.
You use erdoor (wherefore), hierdoor (herefore) or daardoor (therefore) depending on the original preposition+pronoun combination that got changed. Those could have been door het (er), door dit (hier), or door dat (daar).
So, therefore will be something with daar (daarom, daardoor).
We need to learn the difference between due to something, due to that and due to this and to show we have learned it.
It is. :) But your translation is valid as well, although because it is the less used meaning in this kind of sentence, it will only be understood that way with a clear emphasis on hier, in written form: híerdoor (not to clear using this font, but I put an accent on the i).