Where I come from next Sunday is the next Sunday that comes along so I agree with Growler. The Sunday after next is the one following.
I have, over the years, encountered many who would argue as Mrs G does but I have always maintained they are wrong.
So next Sunday follows next Saturday (tho' I concede that since Saturday is in this case tomorrow it could be confusing)
In the Snoopy household (The Daisy Hill Puppy Farm) "Next Sunday" meant the upcoming Sunday but only a few said "the Sunday after next" ... more commonly that would be known as "a week come Sunday" or even "Sunday week".