At parentes earum civitates finitimas, ad quas eius injuriae pars pertinebat, ad arma concitabant.
I translated: But their parents were instigating the neighboring states to arms,for which a part of its injustice was concerning. I am wondering why is a singular form of eius used?
is, ea, id can be used as an adjective to mean Such, of such a sort, character, or quality.
Some context is always useful in these circumstances.
eius iniuriae just means “of this injustice”. It refers to the abduction of the Sabine women.
Your translation of the relative clause is very wobbly. Have another shot at it.
Hopefully this is better: But their parents were instigating the neighboring states to arms, to whom a share of this injustice pertained.