Looking at the family, it is complicated isn't it!
If I'm correct, the 2 children, Herbert William and Beatrice Elizabeth were born long before the 1884 marriage, in 1875 and 1877. They have the surname WILSON, and their mother is called "Honoria Clara WILSON formerly BELL" and father Thomas WILSON on Herbert's birth certificate (on a Public Image on Ancestry). Though the mother was born Rebecca Hartley WOOL - who married Samuel Alexander PARK and then Harry Thompson in 1895. And appears with son Herbert and daughter Beatrice in 1891 as Clara PARK (widow).
"Honoria Clara WILSON" is a vocalist. This sounds like a stage name - there are a few mentions in newspapers of vocalist Miss Clara WILSON around the 1870s, but hard to know if this is the same woman.
I'm not sure that I would assume Samuel Alexander PARK was the biological father of Herbert and Beatrice. Herbert is in the 1881 census as Herbert W WILSON (with Rebecca's sister Rosina and family). And Beatrice is in the 1881 census as Beatrice Elizabeth WILSON (with the LUCKIE family).
Do you have any links to the newspaper articles mentioning vocalist Miss Clara Wilson?
It is very complicated. There was a Thomas Wilson, age 28, born in West Linton, Peebleshire, Scotland, on the 1861 census onboard the Ardent, a Royal Navy ship in Buenos Aires, South America, working as an engineer under chief engineer George Park, Samuel Park's father. No information that he was ever married to Rebecca, and other than that census I couldn't find any information about him.
I can believe that Rebecca really was a vocalist, as she claims on her children's birth certificates. It was very odd for Samuel Park to just disappear immediately after their marriage and never appear with them again, the two children even taking his name, and Harry Thompson was listed as a lodger on censuses before marrying Rebecca after Samuel Park's death in 1994, which presumably they learnt about. Harry Thompson in one newspaper article is described as a Sailor.
It does sound as though Samuel Park worked on ships around the far east and Australia, never as a Captain or even 1st Mate in spite of being qualified with his Masters Certificate. The Wing Sang, aboard which he died in 1994, was apparently a little tea clipper and he was 2nd Mate.
If I knew more about Thomas Wilson, I could see if any DNA matches link to the paper trail. Nothing on Samuel Park DNA match wise, and his extended family tree seems to show a lot of Scottish upper middle class to aristocracy, though his own parents seemed to die in relative poverty, retired in Plymouth, England.
It does look as though Thomas Wilson knew Samuel Park. He definitely knew his father. I actually wonder if Thomas Wilson had died, maybe lost at sea, and Samuel Park knew him, or of him through his father, and knew this so suggested to Rebecca to use his name on her son Herbert's birth certificate. Thomas Wilson would have been 22 years older than Rebecca. The Ardent was in Buenos Aires for some sort of wartime purpose, the Royal Navy was about fighting so loss of life would have been more likely than in the Merchant Navy.