Go here for a better idea of her history prior to new 52/DCYOU. The site is amazing for Titan fans and meshes the retcons together along with creators accounts.
There are a lot of amusing factors with the character especially if you focus on the less confusing aspects. The character came out before Harley Quinn and was actually known as Harlequin for awhile. At one point Two-Face was supposed to be her father that was disappointed she wasn't a twin hence the Duela name. Much like her name implied Duela had two natures, sometimes she was a hero and sometimes she was a villain. She started off as a baddie for Robin/Dick Grayson and there were plans for a love triangle with them and Batgirl. She was apparently engaged to his counterpart (Talon) on her home world.
Tim Drake also had a short encounter with her in Johns alternate future take of the Teen Titans. (*1) He was Batman and Duela had taken up Jokers' role as the archenemy. Neither had any problem with killing. (*2) Her death at the start of Countdown was interesting especially in comparison to her current counterpart in Red Hood/Arsenal. Taking on the role of bad guy once again she decides to kidnap a rich woman only to be stopped by the then directionless Red Hood/Jason Todd. Now back when Countdown was being written there were a lot of ideas floating around. The creative team was toying with the idea of making Jason a strictly good guy again but weren't sure if they should go there. Before Jason could return the woman to safety Duela taunts him on not knowing who he is or where he belongs. Which was also there for an ironic comparison to herself but exchange always struck me.
Because Jason really didn't know where he fit in and the series actually had a moment or two that really underlined his isolation. Of course most of it was terrible still I think it's a nice twist with RHA even though I'm not sold on the current approach quite yet. Both Dick and Tim later confront Jason to blame him for Duelas' death despite having zero evidence. The scene makes all of them--especially Dick and Tim--look petty. To the best of my knowledge Jason never interacted with her prior to Countdown. The Titans despite acting high and mighty have never really been supportive of Duela. But this wasn't their only questionable behavior with past members.
Hell in Johns' TT issue with Jason it turns out Jason didn't even get a memorial despite Dick being the leader. Jason Todd, the guy that stopped Donna Troy from murdering Hawk in a blind rage, helped snap Raven out of her brainwashing and joined them in battle didn't get any respect.
Now I don't know if there's been any attempt by Dick/Tim to help JD in the new universe, I'm not even sure if they met. While I don't feel there's enough to say what direction JD will take quite yet (at least in RHA) I do like the idea that Jason is the one to help. It's a nice flip of what happened in Countdown when everyone expected the worst of Jason and as far as I've seen it's more than anyone else in the family is doing. (*3) I think many people underestimate Jason, his fighting skills, his intelligence and his caring nature. The family it's self is very guilty of this as Jasons' humanity is a huge part of him.
*1 This reality also had Batwoman (Bette Kane wearing Kathys' costume) as Tims' ex. Which is odd since they never said how much older Bette was supposed be. Originally she was Dick's age which could be roughly 7-8 years older. Although Johns retconned Beast Boys' age to make him 3 years older than Tim.
*2 I believe Duela gloated about murdering Alfred before Tim killed her. It's been awhile since I read it.
*3 Except maybe Tim, I haven't been following TT. I know Raven worked with her dad before becoming a Titan.