Welcome to our little gatherine Emily.
I have been discussing this problem with Lesley via email as I think you will be aware.
Seems the big problem is with your William so I am having a deeper look into it to see what I can find.
We know he was born in 1851 although an error was made in recording his father's name when he was baptised.
In 1861 he was at home at Treeve, Sennen with his mother and siblings.
In 1871 he was at the home of his brother James at Bosorne in St Just along with James' wife Sarah and two children.
At this time William's occupation was 'cordwinder' (shoemaker).
As an aside - James married Sarah FUGE at Sennen in 1864.
Sarah was a school mistress born Brighton, Sussex and in 1861 she was boarding at Sennen with John and Caroline TREWHELLA who belong to part of my own family.
In 1881 there is, as has been discussed, a William TRAHAR, married, age 28, a stoker in the Navy who states he is married and that his birthplace was 'Perrouwell'. (I think this will be Perranwell).
Two further points of interest:-
1. There is no record in FreeBMD for any William TRAHAIR prior to 1855.
2. There was a William TRAHAIR who died at Bootle, Lancashire in 1889 at the age of 38 which would be a perfect match for William of Sennen born 1851.
I will investigate this a little further.
William of Sennen was recorded in FreeBMD as TRAHAR.
And there was a William TRAHAR registered in 1852 in the Falmouth Registration District which covers Perranaworthal.
I think this second is more likely to have been the Navy stoker and therefore the man who married Mary Jane Polkinghorne in 1876.
I would think this fellow might be the William TRAHER, age 8, who is living at Perranarworthal in 1861 with parents Hopson and Eliza TRAHER.
The parents are possibly:-
Hopson TREARN married Eliza MITCHELL
Redruth R.D. 1847 March Qtr Vol 9 Page 273
Hopson TRAHER bp. 1st November 1818 Perranarworthal son of Hopson (iron founder) and Mary TRAHER of Perranwell.
Hopson Woolcock TRAHAR married Mary ELLAND 7th April 1810 at Perranarworthal.
Note that Hopson was 'of Perranwell' in 1818 and this is the place of birth recorded for William in the 1881 Census.
The William TRAHAIR who died at Bootle in 1889 is interesting because I can find no trace of the name TRAHAIR or similar in Lancashire in 1881.
That is about all I can do for the moment but I think the only way you can be really sure is to get hold of the marriage certificate.
CT