OK, you have indeed hit upon the researcher's nightmare: the fully documented & published anomaly! :-)
I have here the full catalogue of his works as it will appear in the new critical edition of Clementi's work "Muzio Clementi, Opera Omnia" by Ut Orpheus Edizioni, and that shows op. 37 firmly assigned to what I expect to see it assigned to: the three Sonatas, including the one you so appreciate.
On screen, at the same time, I have the frontispiece to an Edition Durand publication of 3 Sonatinas "op. 37" and 3 Sonatinas "op.38", the ones which evidently are causing you grief.
It's far from uncommon for historical editions of even the most major composers to have anomalies as regards opus numbering between publishers in one country and another. Opus numbers were normally assigned by the publishers in each individual country, leaving the situation wide open to anomalies and errors, and usually with the passing of time these differences get ironed out until they are consistently numbered everywhere. With Clementi having suffered long periods of neglect, it would seem that such a clean-up among opus number assignments has yet to take place -- evidently one of the purposes of the new critical edition currently in progress -- and that has caused the daft situation you have stumbled upon yourself in your pursuit of the actual op. 37 Sonatas.
To solve your practical problem: Henle, under the editorship of Alan Tyson, have published selected Clementi Sonatas in an Urtext edition, and this will give you the G major op.37/2 you are looking for, without those sonatinas getting in your way:
http://www.sheetmusicplus.com/title/Selected-Piano-Sonatas-Volume-II-1790-1805/3765804
(IMSLP, specifically where Clementi is concerned, are in a complete muddle, with two further "Sonatas op.36", the opus number properly assigned to the 6 Sonatinas which every one knows and/or loves from childhood. They too have the op.37 slot taken up by those sonatinas causing you grief, to create even more obfuscation. So no help there, unusually.)
Edit:
Solved!!
A little footnote unravels the riddle of what has happened here with "op.37" sonatinas, as published by Alfred Music Publishing:
"For over 100 years, Clementi's Six Sonatas, Op. 4 were published under the erroneous title, Sonatinas, Opp. 37 and 38. However, when Clementi first published these two-movement works, he called them Six Sonatas for Pianoforte or Harpsichord, Op. 4. These sonatas are excellent follow-up material to the Six Sonatinas, Op. 36, and provide intermediate students with an excellent introduction to the early Classical style. Interpretive suggestions are included." (3)
They also have the complete sonatas published in much less expensive ($12.95) but also less scholarly editions, which will make things more affordable for you:
http://www.alfred.com/Browse/Instruments/PianoKeyboard/Piano.aspx
(just enter "Clementi sonatas" in the search field and they will emerge for you.)
All the best,