Hello again JJ!
'Go' isn't transitive (right?) so I don't see how there can be a direct object in any analysis. What you're looking at here is a
catenative construction, that is, a catenative verb ('go', or in this context, its present progressive form 'am going') followed by a catenative complement (swimming). (Systemic-)Functional grammars such as those from COBUILD then have the concept of
phase ('the meaning relationship between, and structure formed by, a catenative verb and the following verb' - Chalker & Weiner's
Oxford Dictionary of English Grammar (but not the new edition edited by Bas Aarts, which has removed all the phonetics entries and added a lot of syntactic stodge)).
If your example was something such as
I like going swimming (...) then I could perhaps see the point of considering concepts such as gerund (nowadays subsumed by '-ing form' or 'gerund-participle' in most ELT grammars), object etc.
In my topsy-turvy wanna-simplify thinking I sometimes wish even clear participles were simply viewed as gerunds - I am: literally that thing or activity called 'going-swimming'. But that (or at least the hyphenation) is what the concept of phase achieves anyway, so my 'literally that thing called' addition isn't really needed LOL. I wonder if there are any grammars that view the 'swimming' there as some sort of adverbial?
Anyway, the grammars that I consult for this sort of stuff are Chalker's
Current English Grammar, and the
Collins COBUILD English Grammar, and
Collins COBUILD Grammar Patterns 1: Verbs. Unfortunately only the second title is still in print, but the Chalker (which I think you'd find very useful) should be available cheaply enough second-hand on Amazon, and you can get a reasonable idea of what was in the (now rare and quite expensive) Grammar Patterns from the cheap-enough accompanying workbook (
Collins COBUILD Verbs: Patterns and Practice). The University of Birmingham used to have a free online version of the Grammar Patterns (in recognition of the fact that it was out of print but nevertheless an extremely useful publication), but the link (
http://www.birmingham.ac.uk/schools/eda ... index.aspx >
https://arts-ccr-002.bham.ac.uk/ccr/patgram/ hasn't been working for some time.

Perhaps a reprint or new edition is in the works?
