This page imagines a blending between the Worlds of Vampire the Masquerade and DC Comics. The third Robin growing up to be a Vampire Hunter and Batman ans his rogues being vampires is purely my imagination.
Vampire: The Masquerade was a role playing game published by White Wolf Game publishing that gave vampires a society called the Camarilla. There were different bloodlines from ancient vampires. The ancient vampires lent there name to Clans. Most of the gaming took place in cities. So, there were games that would run as (the city) by Night. For instance, you could have New Orleans By Night. The basic premise here would be a fictional Gotham By Night in which the members of the Batman family and his Rogues gallery are mostly vampires.
There is a certain structure to all of the cities within the vampire community. The City has a Prince who rules over the City. The city also has a Sheriff who upholds the law of the Camarilla as well as making sure that the 'Masquerade' stays in place. The Masquerade is hiding vampires from human and other non human eyes. Gotham City would need a particularly strong Sheriff.
Each clan has a representative on the Camarilla council for that city. The representative is the official point of contact for the Camarilla with the clan. They can also serve as the clan's leader. The clans are as follows...
Ventrue - Ventrue are your classic vampires. They are the aristocratic rich vampires who want to wine, dine, and then drink you. They are often haughty and frequently don't understand all of the new ways of this world. Ventrue tend to have a lot of influence and power.
Brujah - Brujah are fighters and not lovers. They are frequently new vampires. They are also brawny, and not always painted as the most swift people upstairs. Brujah are extremely strong and would again rather fight than talk.
Nosferatu - Nosferatu are the worst at hiding the fact that they are in fact Vampires. Nosferatu often live underground or in sewers. They are information gathers and have importance despite their hideous appearances.
Toreadors - Toreadors are the 'artists' of the Vampire community. They tend to be ... well... artistic. Toreadors tend to be a little flaky and hang out in places like Opera Houses.
Malkavians - Malkavians are the 'crazies' of the Vampire world. The last thing you really want is to deal with a Vampire who is out of their mind. Needless to say, Gotham City is absolutely crawling with this type of Vampire.
Tremere - Tremere are the 'magical wizards' of the Vampire sects. They harness abilities in a secret society that some would call... un-natural.
These are not the only type of Vampires which you will soon see. Vampires also have protective servants called ... ghouls. Ghouls have unnaturally long lives but are not Vampires. They have to be fed a certain diet to be kept alive. Ghouls will also protect the Vampires by day.
The natural inclination would be to think of Bruce Wayne as the Vampiric prince of the city. However, Gotham is clearly run by the Malkavians. The Joker (while important) is not a leadership type person as the Joker well knows. That would leave a power vacuum which would inspire the Joker to look for another 'Prince.' The former DA who had recently been horribly deformed fit the bill almost too perfectly. Besides, imagine seeing this as the first site after you thought that you died...
An 'embrace' into Vampireness is not always what you would call a loving experience. Despite flaws, Dent is a natural leader.
The fact that he was driven insane by his disfigurement makes him all the more perfect.
Besides the Joker needs a sense of control over the Gotham sheriff, Dent's transformation as well as the ensuing guilt would be the perfect foil to allow Dent's ascension to control.
Wayne is a defender of Camarilla law. As such, the billionaire is tasked with policing the Vampires within his city. Not only is he not in favor of killing, it also requires an act of the Camarilla council in the city to approve the death of a Vampire. The approval would have to come from a council of Vampires whom are the same people that Bruce frequently has to police.
Bruce must hide his own identity while policing the Vampires of his city. Bruce also has to maintain the Masquerade so that no one figures out we are really dealing with a secret society of Vampires. Bruce has to adopt a vigilante persona which protects both of his alternate identities. As a way to scare both mortals and vampires with a single image. Wayne has adoped the... Batman...
Bruce is protected while in Wayne manor by his faithful Ghoul and butler Alfred.
In addition, Bruce also uses human sidekicks called Robins. The Robins add to the illusion of humanity because of their mortality. After the grow up, there is the potential for the possibility of an embrace. Robins have included Dick Grayson... who seemed destined to be a Toreador...
After Grayson's embrace that made him known as 'Nightwing,' Wayne turned to another young progeny named Jason Todd. Todd was thought to be killed by the Malkavian Joker...
But later came back after a rescurrection by a more ancient Vampire named Ras Al Ghul. Todd would live to be embraced by Al Ghul (who is a member of an assassin clan known as Assamites) trained and embraced as The Red Hood.
With one sucess and one failure, Bruce turned to another as an assistant. The bright young man Tim Drake figured out that Bruce was the Batman. However, he was not bright enough to figure out that Bruce was in fact a vampire. That made Drake the perfect Robin.
Unfortunately, The Malkavian Joker was upset that Bruce would opt for a replacement rather than stopping the Robin program altogether. The Joker's way of dealing with this was attempting to turn Drake (through unspeakeable torture) into a miniature version of himself.
Recovery was equally painful and filled Drake with thoughts of vengeance, not only on The Joker but also on Wayne and all Vampiric society. This would make Tim Drake the Red Robin... feared Vampire Hunter...
Naturally, for his appointed role. Drake's weapon of choice is a bo staff which can also double as a stake... with a lot of satisfying effort. In order to keep tabs on Bruce, satisfy the need for a Robin, and make sure that the Masquerade would not be broken. The assamite Ras Al Ghul created an un-natural progeny for Bruce who would also serve as a sidekick. This would be Damian Wayne. Damian Wayne is the current Robin.
The Malkavian now known as The Joker started out life as a comedian who could not make ends meet.
The Joker attempted to get money and dressed up as a crook called the Red Hood (not to be confused with the Jason Todd version) and was still human when Bruce accidentally dropped him into a vat of acid.
The acid horribly disfigured the Joker. It is not known the Malkavian vampire who embraced the Joker but they must have thought it would make a funny... joke.
The Joker became unstable as well as unpredictable. The Joker eliminated his competition to become Primogen but had no aptitude for actual leadership. This would be when he used influence to install Dent as Prince of the City. Although Dent was a neophyte Vampire, none dared challenge somone with the Joker's support as Prince of Gotham.
Selina Kyle is known as the 'Catwoman.' Selina is the Gangrel primogen of Gotham City.
The Brujah Primogen of Gotham City is a rather large brute called 'Bane.' Do not let his crude appearance fool you. Bane is a meticulous planner and has been rumored to synthesize a kind of hyper-blood known only as 'venom.'
Meet the Nosferatu primogen of Gotham City. This rather nasty customer is named Oswald Cobblepot, otherwise known simply as The Penguin.
This lovely young woman is named Zatanna. Please, be careful. She is the Tremere Primogen of Gotham City and would probably enjoy turning a Prince into a frog.