
WARNING SPOILER ALERT
I have read the novel way back so I don’t really remember what exactly happened before but to answer your question, yes. Chase doesn’t meet Pete until the very end of the novel and I think it’s Josh’s fear of being rejected. Josh arranges a day out for them with Pete, they go to an Amusement Park (?) and there he introduces Pete to Chase as his child.
If I remember correctly, they do have a second child but was later revealed during the epilogue, which was a timeskip after the main timeline (the current story). (⌒▽⌒)

Two reasons: the author tends to add side stories and the universe consists of several stories/pairings.
Yeonwoo and Josh became friends and their children also became friends.
Pete and Cecil appear in several side stories of Kiss me liar (not all are adapted to manhwa so far). Also Angela, the daughter of the pair of Kiss the scumbag is a friend of Spence and appears in a side story.
Why you see more of the children in the KML side stories? Because the side stories of KML take place after the epilogue chapter of the main story.
The side stories of KMIYC so far take place years before thr epilogue chapter, before they got married.
Ok so I have read some comments and they say that chase doesn’t meet pete until the very end of the novel, but how does that work if they have 2 other kids together? Is there a continuation or something