How do you decide when to stick up for yourself and when to let things go? I'm trying to apply Buddhist principles to the way I lead my life, but right now I'm struggling with an issue.
In short, the problem is that someone caused damage to our home and refuses to acknowledge this and pay the damages. The problem is that I'm having difficulty deciding whether to stick up for myself and my family and pursue this matter, or to simply let things be and go on with our lives.

I think there are 2 conflicting Buddhist principles that apply here (or perhaps more, but I just don't see them?): 


One shouldn't attach him/herself (to material matters).
One should move toward truthfulness in all things and correct harm.


I guess what decision to make is somewhat subjective and depends on the exact circumstances, but I'm very much interested in what Buddhism in general has to say about making decisions like this. When should you stick up for yourself and when should you let things be?
you said:


  
  One shouldn't attach him/herself (to material matters).
  One should move toward truthfulness in all things and correct harm.
  


but... the second one does not sound like a Buddhist principle... where did you get that from?

The first one (nonattachment, dispassion) is a universally valid Buddhist principle. As a rule of thumb I would stick with this one.

However, according to training I received, there are two places detachment can come from: 1) from strength or 2) from weakness.


when detachment comes from strength -- it comes from the idea of freedom, of independence, of being one's own island, of needlessness and emancipation, from wisdom, from compassion.
when detachment comes from weakness -- it comes from fear of confrontation or involvement, from laziness, from doubts, from incomplete understanding, from "spiritual materialism", from attachment to private peace of mind.


So you should look inside and see where your detachment comes from. If it comes from weakness then, while on the surface it looks like detachment, it really is a form of attachment.

If that is the case then you should definitely engage with that "someone" - not as much for the sake of what you see as "truth" from your side - as for the practice of overcoming your (hidden) attachment.