This is a story suggestion, one of my better ones: Yeah. Let Batman be in there near the last third of the movie, as a mysterious shadow figure. I'd want MOS2 to be divided up between Clark, Lois, the Daily Planet, the big henchman of Luthor, with Batman being a mysterious character who complicates things.
When the big reveal happens, Batman tells Superman his true intent, and eventually (between blows, the fight is inevitable, and this would be a good way to make it interesting) Superman reveals the truth about himself.
I'd want Batman to mysteriously leave (this can be explained for the sequel), so we don't have an IronMan 2 buddy anticlimax. I don't want Batman saving Superman for MOS2, though I'd want it exactly ONCE for World's finest.
The sales pitch for MOS2 should be
The Day The Earth Stood Still (1950s) meets Spider-Man 2.
A "real world Superman" with an emphasis on Clark and Metropolis, as well as a mysterious, but brazen foe, criminal mastermind, and hidden antihero could make for a heck of story. The key is to "fit in Bruce" in areas that makes sense. "The stranger" could even be a red herring for Metallo. And yes, I want "guess Metallo's identity" to be the subplot of the movie. Weird, I know
The main plot, of course, should be Clark trying to be a part of Metropolis, balance his life as a superhero, lover, and human being. Weaving in the public's paranoia and Luthor's campaign would allow to see the extent of Superman's effect on earth, while showing Clark try to fight that negative image by doing heroic acts and trying to resolve world conflicts.
This higher profile would definitely cause Bruce's Bat-ears to perk up, with the concern that Superman might suddenly snap. When murders from a superpowered villain occur, Superman gets framed, and he must both cooperate with authorities and investigate what's going on to stop them.