there's a clue to their whereabouts in 1861 from the 1871 & 1881 census entries which give the birthplace of some of their children as Scotland. You can get the full details from ScotlandsPeople which is pay to view.
http://www.scotlandspeople.gov.uk/ Have you looked for baptisms for Michael and his sister to see if they are noted as twins? Also, their marriage cert would give Martha's father's details.
Possible from 1841?
Upper Wortley HO107/1350/2 folio 50 pg 19
Jonathan Clough 40 cartwright
Hannah 40
Martha 12
William 10
Sarah 8
John 6
Joseph 2
all born in county
extracted baptism from the IGI batch C071961 for Wortley by Leeds
Martha Clough bp 6/12/1829 dau of Jonathan & Hannah
1851 New Row, Wortley HO107/2314 folio 227 pg 27
Jonathan Clough head mar 54 cartwright b. Yorks, Oldwalton(?)
Ann wife 48 b. Wortley
William son 19 brickmaker b. Wortley
Sarah dau 18 b. Wortley
John son 15 brickmaker b. Wortley
Joseph son 12 joiner b. Wortley
Nancy Hutchinson niece mar 24 cloth ? b. Wortley
Hannah Hutchinson niece's dau 4 b. Pudsey(?)
Richard Hutchinson niece's son 1 b. Pudsey(?)
