There is no such thing in Scots Law as probate, in spite of what sundry web sites (including Ancestry) would have you believe. The corresponding process in Scotland is Confirmation.
A Confirmation in a Scottish court is 'Sealed' in England and Wales if the deceased owned property in England. This is a reciprocal arrangement to avoid the hassle of going through the whole legal process in both countries.
The attached are the images from the original England and Wales Calendar of Probate. (Neither mentions Northumberland; that must be a transcription error. Are you using Ancestry?)
The obvious difference in the names of the persons to whom Confirmation was granted is that the widow isn't mentioned in the second one.
Marion McKay or McGougan died in Prestwick in 1941.
Christina McKay McKinven, mother's maiden surname McKay, was born in Campbeltown in 1907 and died in Prestwick in 2000.
John McKinven married Mary McKay in Campbeltown in 1884.
There's a McKinven household in Campbelltown in the 1911 census index, District 507, ED12, Page 3, consisting of John, 46; Mary, 44; Edward, 24; Neil, 15; James, 13; Mary, 10; Donald, 8; Janet, 6; Christina, 3.
Mary McKinven or Mckay, 48, died in Campbeltown in 1914, mother's maiden surname McMillan. There are several other births of McKays, mother McMillan, in Campbeltown, including Christina in 1874 and Marion in 1877.
So I conclude that the reason why Angus McGougan's estate had to be confirmed twice was that his wife, to whom confirmation was granted in 1940, died before it was fully wound up, and his wife's niece and her solicitor were granted confirmation in 1942. Both confirmations had to be sealed in England and Wales because Angus must have had some property there.
There is no significance in the fact that one confirmation was sealed in London and the other in Llandudno.
I don't understand what you mean when you say that you can't find a definitive death record. Angus McGougan's death was registered in Monkton and Prestwick in 1939.
Check it all out by looking at the original documents at
www.scotlandspeople.gov.uk - and never trust anything you find on Ancestry unless it's an image of an original document.