I am unfamiliar with the mechanical nature of the DCU game, but My recomendation for the vigilantism problem is to come up with a way to reward in genre behavior. Go out of your way to keep your secret ID, get a point. Turn the man who killed your girl over to the cops, earn a point. Etc. This is done in Mutants and Masterminds and I find it works well. It could be something as simple as "plot points" - if the PC goes out of his way to stay with the conventions of a comic setting in an unfavorable way they get a point that they can spend on a favorable plot device. No major changes but things that can help them out. A stray object lying on the ground, a clue, one of the Big Bads henchman owes you a favor for not turning his kid brother in and so is willing to leave the keys to your cuffs unattended for 5 mins, that sort of thing. You can also reward them when you force convention on them liekwhen the bad guy gets away, when he knocks the hero out, etc.
As for Gotham -
What if the Batman Family and all the major crazies are gone? Maybe Brother Eye and his OMAC army got them, maybe something magical happened, no one knows they just are all gone. But there are all of these former henchmen who think they can be the next Crime Boss and have access to all the former baddies old gadgets. This way you can use your own version of the Joker, etc that the players dont know every detail on. They can be definativelly yours. A new crime wave starts and peopel realize that Gotham needs new heroes. Alfred might still be around and uses a file that Batman had on "possible trustworthy allies" plus the Wayne fortune (he would be empowered by a will that Bruce left should he ever go missing and Dick or Tim were also gone) to recruit a new team of Dark Knights to hold the city while the Master is away. That way they have an added degree of accountability with a patron, possibly a mysterious one calling himself "The Outsider", who would enforce on them the Batman Code of Honor. If players didnt want that origin they could be someone who started on their own, or came to Gotham recently, and joins up with Alfred's agents (the other PCs.)
Ease yourself into it. Start with a break in at a WayneTech warehouse with enthralled guards and amok security bots as a kind of "Dungeon". If your players arent interested in doing a lot of detective work (always a problem in my experiance) just hand wave it and say thigns like "after talking to the informant you hear that the new Greenmen (former henchmen of Poison Ivy that worship her like a goddess) are holding a recruiting session in the Park this Friday night at midnight, you are now on the outskirts of the park and ready to go in a bust heads." Do a few Secret ID scenes, some evading of the GCPD, some roleplay with the mysterious benefactor, etc and you will do just fine.
