Theory on story
If you think about the sequence of events until about half way through the trailer, the story has some structure:
It is some years from now, and the Batman has been murdered. Dick Grayson, retired superhero, is out to solve the mystery of his killing. This being Gotham City, there are various and sundry characters involved in a cover-up of the crime, headed by none other than Chief O'Hara. A seemingly retired Jim Gordon has some leads, probably obtained through contacts at the PD, that he passes onto Dick with a warning: he suspects a conspiracy involving some supposedly "retired" super criminals from years gone by. Barbara Gordon, formerly Batgirl, and now married to Dick, refuses to have any part in the matter for the safety of their daughter. It further appears that Chief O'Hara has turned traitor, with plans for "controlling" the rackets in Gotham City through his villain enforcers (Penguin, Riddler, etc.); in return for sharing a large piece of the pie with the villains, he is able to keep them on a leash, and chaos in Gotham City, at a minimum. O'Hara is the head of the conspiracy, aided by Catwoman as his lieutenant, and in his official capacity as police chief tries to discourage Dick from pursuing the mystery of Batman’s death any further. Nevertheless, Dick’s resolve is firm and he takes to the night skies as Robin, smashing through the criminals in his path as he seeks the answers to his questions, and spoiling O’Hara’s master scheme. Once Dick reappears publicly as Robin, however, it triggers the return of the psychopathic Joker...
...and all the while a steely-eyed Clark Kent, in Gotham to report on the death of the Batman, is keeping a careful eye on things...
From here on the rest is conjecture. If I had to guess, I would say that the return of the Joker led to a mass murder involving laughing dolls of some sort. The loss of life hits Superman deeply. Consequently, O’Hara demands that Clark stop Robin before his “heroism” leads other criminals to abandon “the conspiracy” and begin wreaking havoc and major loss of life in Gotham City. This leads to a confrontation between Superman and Robin, which spins out of control when the other members of the Justice League begin taking sides…