I am not a plumber, nor have I done much in the way of plumbing, but what strikes me as odd is the height of the outlet to the main drain. Here is a pic of my kitchen sink plumbing:
Note that the water level will get as high as the base of the main drain. In your daughter's case it looks like the base of the main drain is as high as the "T" (the long horizontal pipe connecting the one drain to the other). So all of that plumbing up to the level of the base of the main drain is full of water (even part of the pipe coming from the dishwasher). I would hazard a guess that this setup doesn't drain very well and allows for a good bit of solid waste (especially from the dishwasher) to just float around in there and cause and rot and cause a stink. Not sure about the gurgling though.