Hi Shauna, I think the Daniel and Catherine on the 1900 Seattle Census could be his second family. I didn't find their marriage in Washington State Digital Archives but they married in 1888 when Washington was still a Territory.
You can contact the Puget Sound Regional Archives, 425-564-3940, or email Archives@bcc.ctc.edu because they have marriage licenses register 1866-1917 and record of marriage certificates 1888-1923.
I did find a Daniel Mahoney in the Washington State Digital Archives who died in 1929 and his birth date is very close to your Daniel's.
I think the son Bernard was Daniel and Catherine's because in 1900 they had been married 12 yrs. Successful Searching!