"He went to his sister's room."
Translation:Šel do sestřina pokoje.
…and “Kateřinin” is a possessive adjective, which is usually formed from proper names; the rules for other nouns seem to be far from simple. I cannot tell you why sestra does not have it; bratr, for instance, does (bratrův).
You often find possessive adjectives in Czech place names, such as Karlův most.