And regarding your idea, I like it. I might do something a little different and move the series in a different direction.
Movie opens with Batman and Nightwing on a rooftop. They're investigating something. Shows that they work well together - both good detectives and good fighters. They end up getting to a place where they can overlook a warehouse where Joker is. Nightwing says they should scope the place out. Batman says he's already sent someone in. Dick is shocked - Jason has only been active for a few months and isn't ready. Bruce says he is. They get in and find Jason dead. Dick runs off, furious. Bruce is devastated.
The Battle of Metropolis. Dick watches. He reaches for his phone. Wants to call Bruce. Doesn't. Months later, another call he ignores from Alfred. Then, as he watches Superman's funeral, one from Bruce. Ignored. All the while, Dick is training. Working the streets. Taking in bad guys. Sometimes, some of Bruce's bad guys.
Present day - Batman takes someone into Arkham. Say...Penguin. Dick watches on TV as the former mayor of Gotham is turned in by Batman. Then the TV goes blank. The feed is cut. The anchors don't know what happened.
The next day, it's revealed that Arkham has been taken over by someone. The police can't get in. There's been no word from the inside. The standoff lasts for days. The media wonders if Batman is dead. Dick can't take it anymore. He collects Barbara. Goes to Alfred. Apologizes. They all go down into the Batcave and find a kid at the computer. They scare him off without getting his name.
Dick and Barbara get a clue from some mysterious source that the siege was done by a mercenary named Deathstroke. They also find, in Bruce's computer, a secret entrance to Arkham. As Dick scopes out the entrance, the kid is there again. He wants to help, but Dick knows (from Jason) that kids can't be a part of this life. He proves it by kicking the kid's ass, hoping he'll learn. The kid runs off, licking his wounds.
With Barbara working as Oracle, Dick breaks in. It's chaos inside as the inmates are running amok. Dick, in his Nightwing costume, battles his way through C, B, and A level DC villains, collecting intel. He hears that Deathstroke has Batman in the main office. Along the way, Dick finds clues and weapons. Gauntlets. Batarangs. Smoke pellets. Just when he needs them.
Finally, right before he reaches Deathstroke, he finds a note from Bruce. He always knew Dick would be a great hero. Despite their estrangement, he's always kept tabs on him. Made sure he was safe. But more and more, he was able to let his protege fly. And now....
Dick finds a Batsuit. Custom fit for him. Putting on the Batsuit, he enters the office and fights Deathstroke. He wins. But Bruce isn't captured. He isn't anywhere. Deathstroke doesn't even know where he is - it's all been rumors.
The movie ends with Dick as Batman. Out of the shadows comes Tim (or Damian), the kid from earlier, as Robin. Dick is ready to embrace the life as Batman, to forgive Bruce and forgive himself. To take up Bruce's mantle and do it his own way. Hopefully, a better way.
Post-Credits - Superman (or Wonder Woman or Flash or whoever) shows up and offers Dick a role in the Justice League per Bruce's request.