Hello and welcome to rootschat!
Henry & Hannah's children (see below) were mostly bp Alderley but some were at Cheadle; their marriages were mainly at Manchester. You should be able to find a lot of the Cheshire records free online on the Cheshire Parish Register Project website, and at least some of the Manchester marriages on
www.lan-opc.org.uk :-
Mary bp 1800 mar John Kinch 1824
Daniel bp 1802 mar Ann Brown 1832
Ann bp 1803 never mar?
William bp 1805 mar Elizabeth ? (from Bangor, Wales) bef 1836
Thomas bp 1808 mar Prudence Unwin 1832
Harriet bp 1811 mar Richard Hampson 1834
Elizabeth bp 1813 never mar?
Henry bp 1816 mar Mary Ann Robinson 1842
Emma bp 1817 never mar
James bp 1822 mar Jane Fallows 1844.
Sorry, but it would take too long to go into all their various offspring!
As for James' dtr Eliza, you have me puzzled... In 1861 blacksmith James & wife Jane + their young dtrs Sarah & Eliza are living with James' wid mother Hannah. I have James dying in 1869, but his widow Jane survived him and in 1871 is living in Cheadle Hulme with children Eliza age 24 (she was bp 1847 Cheadle parish), John Henry 17 and Daniel 14. The 1881 census still has dtr Eliza (34) living with her mother Jane and brothers JH and D.
Mother Jane died in 1887. In 1891 Eliza is again living with brothers JH and D + a Sarah Jane H; likewise 1901; likewise 1911 (except no JH). I think Eliza died later that same year.
But that means that I can't square my version of James' dtr Eliza (1847-1911) with yours (1865-1868)! And I'm sorry but I also can't help with the inquest. But anyway, I hope I've helped you a bit along the way.
Birtle
PS you might also like to take a look at this webpage
http://www.cheadlehulme.net/village/chhenshaw.html Anyway, I hope this helps you a bit. Good luck with your searching.