First, the hormonal and hemodynamic changes seen in hangover are distinct from those seen in alcohol withdrawal, so the advice to drink more is not good, even if some symptoms are in fact improved. See tables 2/3 in the cited review.
It appears the molecular mechanism of veisalgia (HA, a new word) is not well known.
1. acetaldehyde Part of it may be attributed to acetaldehyde but there is clearly more to it. The liver enzyme alcohol dehydrogenase 1 (ADH1) produces acetaldehyde from ethanol, and aldehyde dehydrogenase 2 (ALDH2) makes acetate from that, so the aldehyde does not exist for a long time, and is rather responsible for short-term illnesses.
2. ADH and diuresis
Hangover severity is proportional to antidiuretic hormone
concentration (46). Alcohol inhibits the effect of antidiuretic
hormone on the kidneys, thereby inducing diuresis that is out of
proportion to the volume of fluid ingested. As blood alcohol
concentration decreases and dehydration persists, the serum level of
antidiuretic hormone increases, maintaining water retention in
dehydrated patients with hangover. In our clinical experience,
hydration attenuates but does not completely relieve hangover
symptoms.
3. cytokines
The constellation of hangover symptoms (nausea, headache, diarrhea)
resembles that seen in conditions related to dysregulated cytokine
pathways (for example, in viral infections and after administration of
interferon-alpha). Alcohol alters cytokine production through a
thromboxane pathway. Levels of thromboxane B2 are elevated during
experimentally induced alcohol hangover (42), and the administration
of tolfenamic acid, a prostaglandin inhibitor, at the time of alcohol
consumption has a small prophylactic effect in reducing hangover
severity (9).
4. further substances
Congeners, the byproducts of individual alcohol preparations (which
are found primarily in brandy, wine, tequila, whiskey, and other dark
liquors), increase the frequency and severity of hangover (24, 39,
40). Clear liquors, such as rum, vodka, and gin, tend to cause
hangover less frequently.
So there are factors that aren't even identified exactly, and these could fit the mixing of drinks observation.
There are several reviews out there, just search for hangover at Google Scholar.
Wiese, Jeffrey G., Michael G. Shlipak, and Warren S. Browner. "The alcohol hangover." Ann Intern Med 132.11 (2000): 897-902. Online at http://dionysus.psych.wisc.edu/lit/topics/Hangover/WieseJ2000a.pdf