Just a couple of things, to help eliminate some of the Armstrongs and Dixons:
Regarding the Hannah Armstrong/Robert Dixon marriage in Weardale:
The transcription at FindMyPast shows Hannah's father as Robert Armstrong, and place of marriage as Wolsingham.
Regarding William Ridley Dixon....Although I think we have already dismissed him as a possibility, I am just adding a bit to it. It looks like he married the Catherine Dixon, daughter of William and Ann Armstrong, in Shaddongate. A couple of snips are attached. This Catherine did have a sister Ann, but there was a death notice for Ann several months before the birth of William. This Catherine can be tracked via news articles and censuses, and she never remarried, and as mentioned by Gan Yam, she lived to a good age of 91.
Regarding John Armstrong, brother to Catherine and son of Mary:
Somewhere I mentioned in this thread that he was living with George Andrew and Catherine Watson in a census. He was with them, single, 1901 through 1921 censuses. One identifies him as brother in law to George (the crane driver mast maker). In the 1901 Catherine does put birth place as Lanercost. (20 years later, her birth is listed as "Kind Waters, Cumberland" There is a King Water on the map in Brampton.... )
You already have the middle section of their marriage certificate; I don't know if there would be anything more helpful you would see on Catherine and George's full marriage certificate, other than a possible occupation for her father?