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 µm fine-structure line and underlying dust continuum emission in a sample of seven of the most extremely luminous (EL; L bol ≥ 10 14 L ) Hot DOGs, at redshifts z 3.0-4.6. The [C ii] line is robustly detected in four objects, tentatively in one, and likely red-shifted out of the spectral window in the remaining two based on additional data. On average, [C ii] is red-shifted by 780 km s −1 from rest-frame ultraviolet emission lines. EL Hot DOGs exhibit consistently very high ionized gas surface densities, with Σ [CII] 1-2 × 10 9 L kpc −2 ; 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 2.1 kpc and 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] 500 km s −1 , which on average are larger than optically and IR-selected quasars at similar or higher redshifts. We argue that a possible hypothesis for 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, rather than a continuous single event, the EL Hot DOG phase could be recurrent. The dynamical friction from the frequent in-fall of nearby galaxies and gas clumps, together with the subsequent quasar feedback, would contribute to the high turbulence of the gas within the host in a self-sustaining process that could potentially trigger not only a single, continuous EL event, but instead a number of recurrent shorter-lived episodes as long as external accretion continues.