I didn't assume his family died in the Metropolis stuff. Honestly, I kind of figured that he's a retired Batman, and that note was to taunt him about his guilt over his mom and dad dying. Kind of a "you let your family die as a kid, then Batman left and all these people were killed" thing. Bruce in the comics a lot of the time feels guilty about his parents dying, even though he couldn't do anything. The note could be using that as a taunt, along with the Metropolis stuff, to get Batman to suit back up to take Superman down.
He's desperately screaming for someone to get out of Wayne Financial on his cellphone, then he runs directly into the rapidly approaching debris field to go after them, then he's shown holding a little girl in the aftermath (who could be his or a stranger he thought was his daughter), and finally a newspaper about the building being destroyed has "You let your family die" written on it. That's a pretty strong narrative chain they're pushing on the audience if it's simply a reference to his parents or Robin dying, both of which are also referenced separately in the trailer and provide no reason for him to bitterly resent Superman.
Selina Kyle/Helena Wayne and Talia al Ghul/Damian Wayne would beg to differ.It makes more sense than Batman having a wife and child, which would be extremely out of place for him. I just don't see them doing that.