Census check

[Huwcyn]

That family is # 98 in Ceiri Griffith. The Jane Hughes you refer to above is my 4th cousin 4 times removed !
More importantly, that would make her a 1st cousin once removed of dame Margaret

[grem yn y rhondda]

Huw,  So Lady Margaret and Rev John Owen Criccieth would have been cousins (second cousins?) on the Hughes Derwin Fawr side.
Plot thickens.  I have children of Derwin Fawr as:
1. Catherine Hughes b 1808.  Md Evan JONES
2. Elizabeth (1811-1881).  Md Richard HUMPHREYS (1798-1885) as his second wife (first died young).  One of their sons (Thomas H HUMPHREYS) md Jane OWEN of Gwyndy - one of sisters of Rev John Owen Criccieth (1849-1917).
3. Jane (1814-1895).  Md celebrated CM preacher and scientific farmer Rev John Owen, Ty'n Llwyn.  They had 3 boys and 3 girls - Rev John Owen of Criccieth was their youngest son - not ONLY son as stated in Welsh biography. 
4. Owen (b c 1820)
5. Thomas Derwen Fawr (1821-1893)
6. Humphrey (b1826).  Was helping brother Thomas with Derwi(e)n Fawr farm in early census.

Such talented families - connecting so many lines in Eifionydd.  Liberals and CM in main.  It was my f-i-l's family and his mother Elizabeth Owen 1879-1967 (one of granddaughters of Rev John Owen Ty'n Llwyn and Jane Hughes Derwin Fawr) was put through Bangor University in about 1900 by her childless uncle (Rev John Owen Criccieth) and got an MA.  She was then appointed English teacher in Holywell Grammar School and, before age of 30, was Headmaster/mistress.  Very unusual for a woman in those days.  Despite marrying in her 30's, she later became mother to 5 children between 1913 and 1921.

Getting my interest in family history going again, Huw.  Diolch yn fawr.  Lewis

[Huwcyn]

This is how I see the relationship (If you have Ceiri Griffith, its #27, #98, # 152 - amongst several others)

The parents of Jane Hughes were Thomas Hughes and Margaret Owen. The parents of Margaret owen were Owen Humphreys and Martha Williams.

Owen Humphreys and Martha Williams had a daughter called Jane Owen, around 11 years younger than sister Margaret. She married William Jones (My closest connection to this family)
They had a daughter Mary Jones, who married Richard Owen.
They were the parents of Dame Margaret. The younger John Owen would therefore be her second cousin.

Another son, William, is noted for Derwin fawr, dying in 1830 at 14 years of age.