This is the 2222nd most frequent Polish word.
rodzinnej
"Rodzinnej" means "family" or "related to family" in English.
In this sentence, 'rodzinnej' is an adjective in the genitive form describing 'kolacji' (dinner), indicating that the dinner is related to the family, thus creating the phrase 'family dinner'.
Atmosfera rodzinnej kolacji była niezwykle ciepła.
The atmosphere of the family dinner was incredibly warm.
Here, 'rodzinnej' functions as an adjective in the genitive form qualifying 'miejscowości' (hometown), emphasizing the connection to one's family by referring to the place of family origins.
Odwiedziliśmy muzeum prezentujące historię rodzinnej miejscowości.
We visited a museum showcasing the history of the hometown.
In this instance, 'rodzinnej' is again used as an adjective in the genitive form, modifying 'tematyce' (themes/topics), conveying that the topics are centered around themes pertaining to families.