Bit late to the party here, but it's worth filling in some gaps, if only because this is the top Google result for Robertshaws of Burwains.
Line appears to be as follows:
Ambrose Robertshaw of Burwains (1660-1750) m. Grace Briercliffe?
William Edward Robertshaw* of Yeomans/Burwains (1688-1773) m. ?
Ambrose Robertshaw (1712-1781) m. ?
John Robertshaw** of Coldweather House (1732-1803) m. Jennet Sagar
William Robertshaw of Scars? (1761-1843) m. Margaret Smith
John Robertshaw (1797-1859) m. Ellen Whipp
Thomas Robert Robertshaw (1850-1899) m. Isabella Sutcliffe
Priscilla Robertshaw (1883-1958) m. Thomas Edmonson
* There is a removal order dated 1718 at Lancs. Archives where I believe his illegitimate son William b.1710 was removed from Elizabeth Travis, a papist.
** This John may instead be the youngest son of William Edward Robertshaw.
I have not yet been able to go further back, I wonder if Ambrose was the g.grandson of Ambrose Robertshaw of Heptonstall (d.1616) through his son Jonathan. Hopefully DNA testing will help us resolve this. Also according to his will Ambrose was a tenant of the Manor of Colne, and tracing back through the court rolls at Lancs. Archives may shed more light on his ancestry (see
http://discovery.nationalarchives.gov.u ... /c/F245226).