I am so curious about the personality of Rebecca Hartley Wool, and who these two men were, Samuel Alexander Park, Beatrice's stepfather, and Thomas Wilson, Beatrice's biological father.
I found this on the family search website (from the Church of Jesus Christ of Latter Day Saints).
https://familysearch.org/ark:/61903/1:1:2DJW-T5RIt is the marriage of Samuel Alexander Park to Rebecca Hartley Wool in Apr-May-June 1884, registration district Islington, county London, volume 1B, page 612. Witnessed by Mary Ann Blankey and Robert Murray Hunter.
I clicked Samuel's name for further information about him on this site, and the same man's birth registration Apr-May-June 1851 Greenwich, London, volume 5, page 273, line number 2.
It does look as though this is the same Samuel Park as you mentioned who passed all those seaman's masters certificates, first as second mate and then as first mate.
Rebecca was born in 1854, so she was 30 at the time of the marriage to Samuel in 1884, and he was 33.
Rebecca is listed as a widow in the 1891 census (where her age is given as 32, which seems wrong as she would have been 37). So Samuel Alexander Park would have died some time between 1884 and 1891, but I can't find any reference to a death certificate, though I haven't found a death certificate reference for Rebecca either.
Samuel Alexander Dalton Park was born In Greenwich, Kent, England in 1851 to father George Park, born 1812 in Edinburgh, Midlothian, Scotland, who died 10th March 1891, Plymouth, Devon. And his mother was Sarah Armstrong, born 1811, Coldstream, Scotland, died 1882, Plymouth, Devon.
On the 1861 census for Samuel, he is shown as aged 10, and his mother Mrs Sarah Park age 45, born Coldstream, Scotland. She is listed as head of family, husband away. It is a handwritten document so I struggled to read the husband's occupation, but I think it said engineer. Address given as Lower Maryon Road, Woodland House.
With the Plymouth connection, I am guessing that this Scottish couple moved to Greenwich, where Samuel was born, with the husband's seafaring job.
I felt so sad to think that this wonderful man, Samuel, who worked hard for those seaman's certificates and took on a struggling single woman with two children, giving them his name, just died so soon after qualifying as a first mate.
There seems to be something strange and maybe vulnerable about Rebecca. I did manage to look at the tree you gave me the url to, and Vivien's comments that no father is given on Beatrice's birth certificate, but Rebecca gives her name as Thomasina Wilson. Rebecca seems to have given a wrong age on at least two censuses, and as Samuel's widow is calling herself Clara.
I have pages and pages of notes, and need to think carefully about the information as it has red herrings.
I think the only information I don't already have that would be on Samuel and Rebecca's 1884 marriage certificate would be his father's name and occupation. Which would give the correct Samuel Park.
But the elusive Thomas Wilson is altogether more difficult, and it looks as though people on the Ancestry site have made best guesses as to what was going on.