I think they are connected -- at least according to Tibetan Buddhism, and perhaps according to other schools of Buddhism as well (1) -- and the connection is, as you said, misunderstanding.
Wikipedia's description of the Three Poisons says ...
Of these three, ignorance is the root poison. From ignorance, attachment and aversion arise.
... and gives several Tibetan Buddhist references for that sentence.
(1) "at least according to Tibetan Buddhism, and perhaps according to other schools":
I think that the "three poisons" (including both desire and aversion) are an important or central part of the doctrine of Tibetan Buddhism ... and, that "ignorance" (perhaps what you called "misunderstanding") is seen as the "root" poison from which condition the other two.
That may also be true of other forms of Buddhism too, but I'm not sure. The "three poisons" are in Theravada suttas (sometimes also known as "three fires") but maybe they emphasize craving more than aversion. For example in this Theravada respresentation of the Wheel of Life, the "three poisons" aren't at the centre and in fact "aversion" isn't shown at all. Instead there are several conditions or causes: including ignorance but also desire, attachment, fabrication.
Actually "aversion" seems to be in Theravada as one of the defilements (kilesa) rather than as one of the causes (nidāna).
Returning to the Pali suttas, something like the Vipallasa Sutta: Distortions of the Mind (AN 4.49) warns what the misunderstanding (or ignorance) might be about: that fundamentally it might happen at three levels (perception, thought, and view), and on
three four characteristics (impermanence, dukkha, and anatta, and subha).