||Hot, dust-obscured galaxies (Hot DOGs) are a population of hyper-luminous obscured quasars identified by WISE. We present ALMA observations of the [C II] 158 mu m fine-structure line and underlying dust continuum emission in a sample of seven of the most extremely luminous (EL; L-bol >= 10(14) L-circle dot) Hot DOGs, at redshifts of z similar or equal to 3.0-4.6. The [C II] line is robustly detected in four objects, tentatively in one, and likely to have been red-shifted out of the spectral window in the remaining two, based on additional data. On average, [C II] is red-shifted by similar or equal to 780 km s(-1) from rest-frame ultraviolet emission lines. EL Hot DOGs consistently exhibit very high [C II] surface densities, with sigma([CII]) similar or equal to 1-2 x 10(9) L-circle dot kpc(-2), which is as high as the most extreme cases seen in other high-redshift quasars. As a population, EL Hot DOG hosts seem to be roughly centered on the main sequence of star-forming galaxies, but the uncertainties are substantial and individual sources can fall above and below. The average, intrinsic [C II] and dust continuum sizes (FWHMs) are similar or equal to 2.1 kpc and similar or equal to 1.6 kpc, respectively, with a very narrow range of line-to-continuum size ratios, 1.61 +/- 0.10, suggesting they could be linearly proportional. The [C II] velocity fields of EL Hot DOGs are diverse: from barely rotating structures, to resolved hosts with ordered, circular motions, to complex, disturbed systems that are likely the result of ongoing mergers. In contrast, all sources display large line-velocity dispersions, FWHM[CII] greater than or similar to 500 km s(-1), which are, on average, larger than optically and IR-selected quasars at similar or higher redshifts. We argue that one possible hypothesis that explains the lack of a common velocity structure, the systematically large dispersion of the ionized gas, and the presence of nearby companion galaxies, may be that the EL Hot DOG phase could be recurrent, rather than a single event. The dynamical friction from the frequent in-fall of neighbor galaxies and gas clumps, along with the subsequent quasar feedback, would contribute to the high turbulence of the gas within the host in a process that could potentially trigger not only one continuous EL, obscured event -but instead a number of recurrent, shorter-lived episodes as long as external accretion continues.