Question: If there were two designated survivors (Kirkman and Hookstraten) then why was it decided so quickly that Kirkman would be president instead of Hookstraten?
Answer: While both parties picked a designated survivor, only Kirkman was a cabinet member and in line for succession. Hookstraten was the Majority Whip leader for the House of Representatives and not in line for succession. She would only have become president if something happened to Kirkman.
Answer: The line of succession is VP, Speaker, President Pro Tempore, then the Cabinet Secretaries in the order the department was created. If none is qualified, then the Chief Justice or senior member if no Chief or Chief is ineligible or declines, acts as POTUS until either the House chooses a new Speaker or the Senate chooses a new Pro Tempore, whichever is first.