From Eric Partridge, A Dictionary of Slang and Unconventional English, fifth edition (1961):
apple-sauce. Impudence: mostly lower middle class: late C.19–20. An elaboration of sauce, n., 1 ...
The relevant definition of sauce in Partridge is as follows:
sauce. Impudence, impertinence: coll[oquial] and dial[ectal]: 1835, Marryat (OED); perhaps much earlier (see [more] sauce than pig [defined in its own entry as "(To be) very impudent, impertinent: coll[oquial]: late C 17–18. B[ritish] E[nglish]"]. Ex saucy ...
J.E. Lighter, The Random House Historical Dictionary of American Slang (1994) offers this more elaborate, two-definition entry:
applesauce n, 1. Theat[rical] silly trite comedy [Citations, starting in 1918, omitted.] 2. nonsense, flattery, insincerity; lies—also used as interj[ection]. [First two citations:] 1919 T.A. Dorgan, in Zwilling TAD Lexicon 15: They spill a lot of applesauce about big money, 1920 in Collier's (Jan 1, 1921) 18: That's all apple sauce!
So applesauce, as used at the end of the OP's quotation simply means "baloney!"
A Google Books search doesn't find the Dorgan/Zwilling example mentioned in Lighter, but it does find two instances (both by the same author) from Collier's Magazine in 1921. From H.C. Witwer, "Auto Intoxication," in Collier's (January 1, 1921):
"Gimme my money back, you burglar!" shrieked the newcomer, ignoring me entirely. "I'm gonna have you pinched. This old tomato can is nothin' but a mess of junk! When I cranked it up last Friday mornin' the rear end fell out in the street, and the repair man tells me the only reason it ever run a foot is because you went to work and doped the motor with ether! The bearin's is all shot, it needs—!"
"Ssh!" interrupted the dealer wearily, as one who hears an old story. "That's all apple sauce! I told you the job needed the touch of a monkey wrench here and there. You can't expect to git no factory pet for what you paid for this car. They's no use gittin' hysterical, you bought the car as is, and they i absolutely no comeback. If you don't want it, leave it here and I'll sell it for you some time to-day and git you what I can for it!"
And from H.C. Witwer, "The Shooting Stars," in Collier's (June 11, 1921):
"A thousand pardons, old man!" says my vis-a-vis, climbin' out into the road. Dug, he didn't look so particularly hugely when he was scrunched up behind the steerin' wheel, but when he stood up and unfolded his full length, it was different. "You were hitting it up so fast, I had no idea you intended turning off the road here," he goes on. "However, I'll—"
""That's all apple sauce!" I bellers, steppin' over to him, "A guy drivin' a can like yours should be prepared for anything, and they ain't nobody in the world goin' to run me down and get away with it. Put up your hands, you big stiff!"
These are the earliest two matches in Google Books search results, although the expression is quite common by the mid-1920s, it's euphemistic qualities making it a favorite choice in periodicals such as Boys' Life.
The OED attributes haptic and haptics to translations of a passage in Isaac Barrow's 1683 Lectiones Mathematicae,
Quod si perinde comperta foret undulationis aereae figura, qua sonus efficitur, et audiendi sensus impellitur, inde nova proculdubio pars emergeret Matheses, Acoustices nomine celebranda.
Haptice quoque, et Geustice, et Osphrantice pari jure mererenur in hunc ordinem cooptari; si cujusmodi motibus peraguntur istae sensiones conjectura subodorari possent philosophantes.
The first citation of haptic in the OED is from 1860, in William Whewell's edition, and the first of haptics in an earlier translation published in 1734 by John Kirby:
But neither term saw much light of day, and it is more probably more accurate to say that it was introduced from the world of psychology in the late 19th century, the OED's second suggestion. Specifically, it appears the 1892 Über den Hautsinn by Max Dessoir, coined as a parallel to acoustics and optics:
Ich erlaube mir, hierfür das Wort „Haptik" in Vorschlag zu bringen, das im Anschluss an Optik und Akustik gebildet und von dem Verbum ἁπτομαι abzuleiten ist.
or loosely,
I take the liberty to bring forward the word haptics in proposal, which follows optics and acoustics and is derived from the verb ἁπτομαι.
I imagine Dessoir wanted a term of Greek origin, hence haptics over, say, tactilics. Haptic as an adjective is cited from 1895 onwards, with the first post-Dessoir citation given from Mind 4:407:
In haptic sensations are recognised sensations of simple pleasure, of traction and of impact.
Until the term was applied to touchscreen technology, the psychological term seems to have been the principle use, hence the International Society for Haptics.
Best Answer
Nobody can say when -- or where, or by whom -- this usage came into existence. It's probably been around in one guise or another, in English and its ancestor languages, for thousands of years, because it instantiates a widely used and very important Metaphor Theme. There are a number of concepts converging here.
Go is used because it's part of the Path Metaphor for communication (which in turn is part of the Conduit Metaphor theme).
Go (a Deictic term, semantically related to come, bring, and take) means, initially, to move away from where one currently is located. Maybe directed toward someone else, or maybe just out.
Messages of all sorts go forth from a source. In particular, sounds go forth. Go is often used in children's language to refer to the stylized sounds that common animals make:
So it's a very small step from
to
and in fact, just another small step from there to