Is there an instance where the sun sets or rises partly, then return back?
Yes, such sunrises happens every year at the beginning and end of the polar nights at high latitudes. One can have a few days with a glimpse of the sun but disqualified sunsets and sunrises. 

Sunsets occur at the end of the midnight sun period by the end of the summer, the first sunset is not complete. 


Sun at it's highest elevation at midday. (To be honest, the picture might be taken the day after the first sunrise, as some mountains are hiding the horizon.) 

Here is e.g. an article from Svalbardsposten, the northernmost newspaper in the world, reporting of the first rays of sunlight after the polar night and some pictures from the last sunrise/sunset before the polar night in northern Sweden. 

The same occurs at the southern polar circle and south thereof, unless it's cloudy... 



Update: here is a great time laps from Davis Station in the Vestfold Hills showing exactly what you asked about: Mid winter