Hi
Now I've had chance to digest the information it seems to me that Peter Baguley (son of Thomas and Ellen) is the most likely candidate to be father of the grandson Richard who appears in the 1861 census.
Richard was born in 1853 so if I'm right Peter should be around in the 1851. I wonder if you would mind checking this out for me? Richard's birthplace is given as Appleton so hopefully his parents didn't stray far from the area.
You may well be right about Richard being the son of Peter (c1826) but my money would be on him being an illegitimate son of maybe Sarah or Ann Baguley.
I have searched around the 1851 for the above Peter however I did not find him, you may have to wait for the 1851 to be indexed nationwide and put online. Or have a go on the Lancs board for a 51 lookup.
I did find Richard in 1871 working in Great Sankey Warrington as a farm lab RG10-3902-F45 indexed as Baynley.
As for the other Peter he his in Lymm with his children but I cannot find his wife.
HO107-2163-F79 Broom Edge LymmPeter Baguley head marr 32 lab Lymm
Sarah daug 7
Thomas son 5
Joseph 2
Harriet Borrowly ? lodger 20 fusion cutter Lymm
I have found Sarah Baguley also in 1851
HO107-2203-F480 45 Haydock Street WarringtonMargaret Ann Wright head wid 44 shop keeper Warrington
Robert son 14
William 13
Elizabeth daug 11
Richard son 9
Sarah Baguley servant 18 Stockton Heath
bye for now
peterbennett