Aha. The supposed inlaws in 1881 are actually Arthur's mother and stepfather.
Mary Milton married Alfred Merriman in Nottingham in 1866.
In 1871, they are in Snenton:
Alfred Merryman, 53
Mary, 47
Alfred Henry, 24
>> Arthur, 14
Elizabeth Needham, 44, wife's sister
So here is a possible alternative name for Arthur. I don't see any likely trace of him under that name yet though.
Finding Arthur in 1861 seems to be key, but I can't. I've ruled out Arthur Needham son of Henry and Mary, and Arthur Redmile, son of James and Mary, by other conflicting records, I think. In 1861, there are five Arthurs with mother Mary in Snenton born c1860; I haven't checked further on them because my fingers are freezing and I'm going to go make supper!