▶ Homework
According to the OED, the original meaning of "homework" does conflate much more obviously with "housework," with the former being defined, above all, as:
Work done at home, esp. as distinguished from work done in a shop or factory.
The earliest citation is a hearty piece of precious advice from a sermon from the 1680s:
Wherefore let every Man, in the first place, look after his Homework; what he hath to do at Home.
Less vague examples of homework were given in later quotes: Spinning, quilting, and embroidery. This crafty and practical usage seems, however, to be an obsolescent meaning of homework, with the last use from the '30s. But the word "home worker" (doing low-paying piecework) lives on, preserving this original meaning of "homework":
Most home workers are women. They need the flexibility of working hours that home work allows. (Guardian, 1973)
The second—and now primary—meaning of "review/preparatory school work despised by youth" didn't appear until much later (late 19th century), but it's thriving and strong, having quickly overtaken the original meaning.
▶ Housework
The first citation of "house-work" from the OED (which hyphenates it) is from mid-19th century. Its meaning has always been as it is now: "the work done to keep a house orderly (and housewares clean)," diligently by housewives and begrudgingly by house-servants:
While the boys are engaged in out-door work, the girls could be employed in sewing or house-work. (Report of the Commissioner of Indian Affairs, 1871)
Here it contrasts homework (sewing) with housework [other activities].
As FumbleFingers's Ngram shows, it has also been used in texts in its unhyphenated form, which the OED has chosen not to include, as Alenanno first noted above in the comments, although it does feature a sub-entry for the spaced "house work" (definition-less, with a single late-19th-century quote).
So the two words would seem to have diverged after the first (homework) took on a specialized meaning relatively late in its life. Now let's find the courage to get back to doing either/both!
According to the Oxford English Dictionary, the etymology for trumpet is:
Etymology: < French trompette (14th cent.), dim. < trompe , trump n.1
In addition, EtymOnline adds:
c.1300, from O.Fr. trompette "trumpet," dim. of trompe (see trump (n.2)). The verb is recorded from 1520s; figurative sense of "to proclaim, extol" is attested from 1580s.
The etymology for triumphant, on the other hand, is:
Etymology: < Latin triumphānt-em , present participle of triumphāre to triumph v., or < French †triumphant , triomphant (15th cent.): see -ant suffix.
For this, EtymOnline adds:
late 15c., from L. triumphantem, prp. of triumphare (see triumph).
This does not suggest a direct relation between triumph and triumphant, as the words they can be traced back to differ. Perhaps the French trompette is indeed related to the Latin triumphant (thus giving an older and shared French root), but the OED provides no further history. So, because the two words can be traced back to different French roots, they have different etymologies in English. This does not mean that trompette and triumphant don't share a root in French, but as far as English roots go they are different in this regard.
Best Answer
No one really knows why they're called dongles. An early dongle was a "solid and non-dangling RS232 block", and it's only really modern dongles that dangle, and only then when attached to a key-fob or lanyard. A claim they were invented by "Don Gall" was just made-up for an advert.
However, we do know the computer dongle now often refers to a USB memory stick but earlier dongles were hardware security devices, without which a software program won't run. Security dongles are still used and often connect via USB. I've used serial-cable dongles, but more recently they've been USB (because more computers have USB than serial connections). It doesn't matter who copies the software: without the physical dongle, you can't use the software.
OED
The definition in the OED is for a security dongle:
They say the etymology is "Arbitrary".
Wiktionary
The meaning has passed on from a hardware security device, to any [USB-based] hardware security device, to almost any [USB] device. Wiktionary has two definitions, the first newer and more general:
Both of these say the device interacts with the computer ("alters its functionality" or for "copy protection"), but I think it's also used much more generally as any smallish USB-based connecting thingy.
Jargon File
The earliest Jargon File entry is in version 2.1.1 of 12 June 1990:
In the latest version 4.4.8 the definitions have expanded:
And:
Language Log
Language Log, the linguist blog covered dongle and agree current use is more general:
The comments includes this from Peter Jackson that points out early dongles were far from dangly: