We went swimming later in the afternoon, Jack and I
This sentence has been done something to.
It's an example of the syntactic rule of Right-Dislocation.
The sentence it's transformed from is Jack and I went swimming later in the afternoon.
The rule copies an emphasized Noun Phrase (which may be subject, object, or oblique)
in a sentence, and repeats it, with a different intonation, for emphasis, at the end of the sentence. It's not a movement rule, but a copying rule, since the original NP remains in place as a pronoun.
(There's also a rule of Left-Dislocation, which copies the NP to the beginning of the sentence.)
Here's the entry from Haj Ross's list of The Top 200+ English Transformations
(p.4, categorized under "I. Emphasis; A. Pseudoclefts and Dislocations")
"6. LEFT AND RIGHT DISLOCATION:
My horse snores. ➞ My horse, he snores. (via LEFT DISLOCATION), or
My horse snores. ➞ He snores, my horse. (via RIGHT DISLOCATION)
In pseudoclefts, this rule will produce related sentences like the following:
Anne's brother left ➞ Anne's brother is the one who left ➞ Anne's brother, he's the one who left."
Some more examples of dislocated sentences:
- My Uncle Will hates the Dodgers a lot. (Base sentence)
- My Uncle Will, he hates the Dodgers a lot. (Left-Dislocation of Subject NP)
- The Dodgers, my Uncle Will hates them a lot. (" of Object NP)
- He hates the Dodgers a lot, my Uncle Will. (Right-Dislocation of Subject NP)
- My Uncle Will hates them a lot, the Dodgers. (" of Object NP)
As for why anyone would think any of these are more or less "formal" or "old-fashioned"
than others, I can't really say. "Formal" and "old-fashioned" are not linguistic terms,
anymore than "fad" or "fancy". Everybody has their own idea(s) about these terms.