Dual Dream Dimensions Disorient Dogooders

The Dream Dimension was first discovered by the Flash when he perceived of its existence as a band within the velocity spectrum, which he physically entered while approaching and surpassing the speed of light. This reality had previously been accessed mentally through the Amazonian Memory Chair, a devise developed on the Paradise Island of Earths One and Two, as well as the Kryptonian Symbioship which Zor-L of Krypton-Two designed.

Sometime after the Earth-One Flash ventured there, scientist named Doctor Sanford Garrett developed equipment in conjunction with the United States government allowing him to physically travel within that dimension. Offering to test this himself in order to save a high ranking official trapped within through his dreams, Sanford adopted the alter ego of Sandman, with the mission of protecting humanity from nightmares manifested therein. Sandman could only return to his home world of Earth-One one hour each day. 

Sandman eventually met the Flash and his teammates in the Justice League of America, while battling the dream-themed villain Doctor Destiny (a similar tale  involved the Justice Society vs Brain Wave). Among those present on that case was Wonder Woman, whom Sandman had previously observed from his Dream Dome and cultivated romantic feelings for... which were not reciprocated.

Interestingly, both the Wonder Woman of Earth-One and Power Girl of Earth-Two had partial existences within the Dream Dimension while mentally linked to the Memory Chair and Symbioship, wherein they had fabricated lives and adventures.  As virtual representations of themselves, these women experienced stories within the Dream Dimension that mirrored the real life tales of their cosmic twins, Supergirl of Earth-One and Wonder Woman of Earth-Two.

While the Earth-Two Sandman, Wesley Dodds, did not have direct access to the Dream Dimension as had his Earth-One doppelgänger Garrett Sanford, he did have a strong connection to dreams which he relied upon in his various adventures as a costumed crusader. Unlike Sanford, Dodds kept his relationship professional with his Justice Society teammate Wonder Woman. No doubt, his having a true love in his own dream-girl, Dian Belmont, helped him avoid looking at other women. Dian's own cosmic twin, Beautiful Dreamer of Earth-Two, also had a connection with the Dream Dimension from which she derived her powers.