Spoiler
Because at first Josh didn't tell him that it was their child, Chase was mostly nervous around Pete.
Then Josh left Pete and Chase alone so they could bond but Pete got distracted and ended up in a really dangerous situation.(It involved dogs)
Chase immediately began panicking thinking it was Josh's son.
When he learned where Pete could have gone, despite knowing that there were probably dogs there, he still went to rescue Pete.
Then things happen and Josh saved them both at the nick of time.
That's when Josh told Chase the truth and Chase's rxn was pretty positive and they cleared up all the misunderstandings.
And then...Josh proposed to Chase. Though it was at the very end of the chapter so it wasn't too elaborate, I would say it was exactly the kind of proposal I expected from Josh.
After that we get extras after a few years of time skip.
SOMEONE SPOIL ME RIGHT NOW, WHAT WAS CHASE'S REACTION TO PETE???