What is the mechanism behind unihemispheric sleep in animals?
In general, I don't think the answers to these questions are known.  This paper is a good review of unihemispheric slow-wave sleep (USWS); the section on neurophysiological mechanisms is largely speculation based on how slow-wave sleep is generally thought to function--despite its lack of answers, that section is good reading anyhow, since it covers current evidence (in 2000, anyway!) and lines of inquiry.  I dug through its citing articles as well, hoping for a more informative update; the best I found was this paper, which shows small differences (which may or may not be statistically significant) between the openness of the ipsi &amp; contralateral eyes to the sleeping hemisphere based on right/left--which does suggest at least some hemispheric dominance at play. Eared seals also sleep on their side during USWS, and leave the sleeping side of the body out of the water, while the awake side of the body paddles to keep their nostrils from submerging; I found nothing suggesting hemispheric dominance issues there, though.

As far as hemisphere-switching mechanisms go, that first paper mentions work finding that unihemispheric slow-wave sleep develops only following sagittal transsection of the lower brainstem in cats--even when the interhemispheric commissures were not involved; that implies some kind of uncoupling of lower brainstem sleep regions, but that's about as far as anybody's got (or as far as I could find!).

An interesting question!  If you find more work, come back and tell me about it.

References
1 Rattenborg, Amlaner, &amp; Lima (2000). Behavioral, neurophysiological and evolutionary perspectives on unihemispheric sleep. Neuroscience &amp; Biobehavioral Reviews Volume 24, Issue 8, December 2000, Pages 817–842.
2 Lyamin, O., &amp; al. (2002). Unihemispheric slow wave sleep and the state of the eyes in a white whale. Behavioural Brain Research Volume 129, Issue 1-2, 1 February 2002, Pages 125-129.