I believe it has been established that JTK has only one nephew. If I'm wrong, I'll be sure to hear about it.
That's ambiguous. "What Are Little Girls Made Of?" stated that George Samuel "Sam" Kirk had three sons. "Operation -- Annihilate!" later claimed that Peter Kirk was Captain Kirk's only surviving relative. Some fans have resolved the contradiction by assuming the other two nephews died sometime in the few months between those episodes, or that they died in the parasite attack but somehow went unmentioned. But several previous tie-ins have ignored the line from OA and depicted Kirk's three nephews. Bottom line, it's a continuity error and there's no consensus on how to resolve it.
Trek works best if you look at it as examples from all the various universes. In Universe #1285 JTK has three nephews. In Universe #250 he only has one. In a similar fashion Universe #29042 we see a James Kirk with the middle initial of R. There are no continuity errors, just an infinite numer of universes, some quite similar, some remarkably different.
The run from TOS through ENT are fairly similar in their history. The 2009 movie is much more removed but still using the broad strokes.
It all fits.
Bashir: What I want to know is, out of all the stories you told me which ones were true and which ones weren't?
Garak: My dear doctor...they're all true.
Bashir: Even the continuity errors?
Garak: Especially the continuity errors.