Good to hear from you. Obviously, it is not 100% yet, but it seems very very likely they are related, in which case you have got a close connection with my Stephen Gaudern who married Frances Weldon. Their daughter Frances (19 July 1763 - 8 March 1851) was widowed by 1851 and childless (she was the third wife of my ancestor who was her first cousin) and aged 87. Harriet Gaudern's father William of South Kilworth was her Administrator, aged 73, so he must have been closely related. The dates I have for the family suggest a younger brother is 100% more likely than a nephew. He might have been a cousin I suppose (less likely).
I am very puzzled by this branch of the family. The Weldons were well to do and London-based who married into the very-well established and landed family of Jackson of Duddington (hence their presence in Duddington), and yet there is a Weldon Gaudern, who can only be a grandson of Stephen and Frances with an unusual name like that, who was a Gamekeeper. And all the Gauderns I have found at Apethorpe (by surfing the web), who definitely bear the same family Christian names that repeat and repeat amongst my Weldons, seem relatively impoverished and close to the land.
So on the one hand, there are a whole load of closely connected Gauderns, some of whom are farmers of very few acres, others gamekeepers and others agricultural labourers, and yet Stephen Gaudern had Weldon nieces, who married into the family of Marsh/Fludyer, several of whom were MPs and one was Lord Mayor of London, who left an estate of £900,000 in 1768!! (He was a clothier and then Deputy Governor of the Bank of England)
It may simply be the difference between town and country at that time. It was not a good time to have your wealth tied up in farming.
Quite a few of the Weldons left wills (and I think there are more to be found) with bequests to their Gaudern nieces and nephews, so I will let you know if I find anymore
All good wishes from Sleepless 2!
