Yesss the kid does accept Chase as his father though it was not shown in the main story and only in the side stories. Josh suggested Chase to spend a day with Pete alone. The father son was really awkward with each other at first but later on when Chase fainted (they went to a pet store because Pete likes dogs and Chase has phobia with dogs but kept silent about it because he wanna do what Pete wants) so yeah Chase fainted and Pete then said if his Daddy doesn't like dogs and then he also doesn't like dogs Josh and Chase were shocked how Pete knew Chase was his Daddy and Pete said because of the hair lmao. (Chase kept his black hair throughout the entire main story)
Was too impatient and decided to read the novel lol. Now....who wants spoilers