Yes, I'm familiar with your predecessors, your Thomas Acton was the brother of my great great grandad John. He was christened at St Katherine's in Blackrod on the 1/1/1837 and married a woman called Mary who passed away on the 13/6/1870 leaving him a widower. Thomas worked as a coal miner like many people living in the area at the time. Sarah is the only child of his that I know of but it is possible that there were others an I haven't found them because I wasn't looking for that particular line. Sarah didn't marry until after her first child (Martha) was born on the third of August in 1883. She was still listed on the census of 1881 as living with her father Thomas then. According to later censuses she had two sons Ralph (c.1887) and James (c.1890) Green so must have been married by 1887. (Martha is listed in all the census returns as Marth ACTON).
Martha was also the name of Thomas Acton's mother (who was more commonly known as Matty) she was christened at St Katherine's on 6/10/1816 and was never married. So far as I know, Thomas and John were her only surviving offspring. She died in Blackrod and was buried there on 18/12/1877.
Matty was the eldest child of Thomas Acton and Nancy Bean who married at St.Peter's in Bolton on the 20/11/1815 (at the time St Katherine's was not licensed to perform marriages) Nancy was Thomas's second wife, his first wife Mary Coulson died that same year. Matty had two sisters and a brother that I know of (Mary, who died aged 12, and Fanny who later married Robert Speak and was the mother of Ralph (1848) Nancy (1851) William (1856) and possibly Elizabeth (1860)).
As I have no information on what happened to Sarah Green (nee Acton)'s children it would be interesting to hear what you have got. When did the family emigrate, for instance? I think that now there are branches of this family all over the world as they were definitely wanderers.
The furthest back that I can take the family is to William Acton who married Martha Farringdon on the 21st May 1760. I think he must have been the grandfather of Matty Acton. Some of my older relatives think the family came over from Ireland in the 1700's, probably to work on the canals. (William was an engineer, a specialised profession in the 18th century).
Please e-mail me your details and I will try and scan my charts and send them back to you ASAP.