Pecker testified that Trump was not worried about the embarrassment to his family, but was worried about the upcoming election.
After the election, Pecker and Trump had a short meeting. In that meeting, Trump thanked him for handling the McDougal and Doorman stories.
Steinglass asked him what Trump meant by that.
Pecker said he thought Trump meant the stories would be "embarrassing to him his family, and the campaign"
Steinglass asked him Trump had said anything about his family, and Pecker said that his conversations with Cohen and Trump were about the campaign, they didn't mention his family, and he (Pecker) made the assumption that the concern was for the campaign.
Steinglass then handed Pecker a copy of his non-prosecution agreement with the DOJ and asked him if that "refreshed his memory".
Pecker then said that prior to the election, Trump was always concerned with how a negative story would affect Melania or Ivanka or his family, and after Trump's candidacy was announced his conversations with Cohen and Trump didn't mention the family.
All of that testimony was Pecker's own assumptions, not something Trump or Cohen actually said. (pages 1217 and 1218 of the transcript)
Pecker's dealings were with Cohen. He only spoke to Trump a few times, and very briefly.
Pecker pitched the idea to Cohen and Trump about killing negative stories- it wasn't Trump's idea. Trump told him "I never pay for stories, they always come out anyway". Pecker and Cohen talked Trump into going along with it.
Cohen didn't work for the campaign. Trump's involvement was basically just being informed after the fact about the stories.