Going to the US with TK hasn't been that easy for us - not sure because we travelled with kids.
When we got to IST - at the gate to IAH flight we were asked for our return tickets print out. I said I have it electronically and he could also call the PNRs to see the e-tickets. Then he said where's our ESTA approval print out - I said we don't print it out as you can also see if it's approved or not. I had a screenshot in my laptop and I told him that I can show him that if he needs to. He called someone and after a while he let us through.
Then of course we were subjected to extra screening - all the pax with kids were told to do secondary screening. I flew with SK ex-CPH and none of this ever happened to us.