The deceitful uses of trump variants apparently come from the French tromper, but this itself almost certainly comes from trompe, which comes from Germanic & means trumpet. The OED reckons it's probably a word with an onomatopoeic (now there's a good obscure word!) origin. It's imitative of the sound, in other words. Remember also that, back then (we're talking middle ages & earlier), the trumpet would not have been the orchestral instrument we know today.

I suggest that such usage comes from the notion of a loud blast with not necessarily very much behind it! Similarly the other use of trump (which I think derives from cards, primarily) can also be traced back to trompe i.e. the sense of over-riding / over-topping something else (loud blast of sound again). Finally, Trump (and Trumper, as in Victor Trumper, a famous Aussie cricketer of many years ago), according to a wiki entry is /was a maker of trumpets. Donny boy just blows his own...