What did John want Connor to say...

Maybe he called Conner out because of his smug, off-hand remark..."two wakes in a month"
Apparently, he always had a problem with jumping the gun (no pun intended) and his dad was trying to make him aware of it...trying to get him to be SINCERELY sorry...more humble.
Not sure if this helps, but hopefully you'll understand what I'm trying to say.

As I just re-watched this movie:

re: "I would like to apologize for what happened,"

Conner made it sound like his apology was optional, saying, "I would like to apologize..." His father's reaction was the equivalent of saying, "I don't give a damn WHAT you'd "like to" do -- you are going to give a sincere apology whether you'd 'like to' or not."

I love that scene. There is a proper way to apologize, and the graver the offense the better the apology better be. It's not like your shopping cart bumped someone else's and an "oops. Sorry!" isn't good enough. And as said, saying, "I'd like to apologize" is worthless. Then apologize. This is how you do it: https://www.mindtools.com/pages/article/how-to-apologize.htm

I think the guy Connor and Sullivan were questioning was going to spill the deal Connor had going with Nitti and THAT was why he shot him in the head forcing Sullivan to take out the others

John may have known about it or suspected it

THAT is what John Wanted to hear, WHY they went to talk to someone and ended up killing 1/2 a doz.

TRY AGAIN

JOHN was at the point he couldn't trust his son

Another point --- WHY was Nitti protecting Connor if they didn't have a deal of somekind

‘If we have sex we will become John Connor and save the world from Skynet. Start to undress…’