The answer to your question 'why do both the Wagstaff boys have Stubbs as their middle names?' is because it was their mother's maiden name.
I've also found that marriage for Mary Stubbs to William Corbishley 13.1.1811 at Prestbury.
It's on familysearch - you can search on there for a marriage with the name of a spouse, which you can also do on findmypast if you go to 'advanced options'. You can see the actual images on familysearch and findmypast.
He was a dyer in Macclesfield. There are no ages given in the register, but she is given as a spinster.
You need to look for the burial of William between 1811 and 1834, and any children born to him and Mary between those dates.
Surprisingly, there are many burials for William 'Corbishley' between those dates. It looks like several of them were children. I've looked at some of them, but this needs more in depth research.
Beware there is one burial in 1830 in Macclesfield which looks promising as on the transcription it says aged '56', which when you look at the register actually says 'inft' - infant. (!)
As to being given as 'servant' in the Census, remember nothing you read in a record, especially a census, is set in stone. Ages can be wildly out, places of birth miles away. names changed for whatever reason.
I have an ancestor who is also given as a 'servant' to the head of the household, when I know for a fact he was his grandson.
So always take any information with a good punch of salt.
I suspect if you dig deeper into Mary Stubbs, you will probably find the Matthew Stubbs they were living with in 1851 was her brother, or other member of her family.
