If anything I'd want to do something where it's evolved from just one man in a suit, and to give everything a different dynamic than just what they got before with some different people.
Actually...you know what I'd like to do as a trilogy? Jump way forward with each installment. You're in Batman Beyond-ish time by the second, then way into the future by the third. That way you're really evolving the ideals and legacy of what Batman established, and spanning truly epic measures of time with each prior story really being the stuff of legend to the next.
Love it.
First movie is set five years after TDKR. After Blakes training, hes around 30 years old maybe fighting in a Nightwing esque identity. A Batman Beyond suit is teased at the end. Barbara Gordon falls in love with him, she's the Oracle.
The second is like Beyond. But several years later. He's at the end of his time as Batman and he's passing the torch but he could be choosing a few kids from the orphanage.
The third would be set into the distant future. Kind of like what u said, but 20 years later (would place it at the year 2050 about), and what Gotham is like and how Batman as a symbol has progressed would be the main topic. It's like a League of Shadows of their own but with completely different methods of course. Bruce could be in his late 60s..and maybe he comes back to Gotham, and the sons of batman have become too violent or something. Blake has died. So, he's back like an older Ra's to teach them what it's all about.
Since Blake died (Bruces successor) there's a whole League but they dont have much direction. They've steered away from Bruces original intention, some are around but too violent like Azrael/Red Hood kind of behavior. Some have been sucked in by the mob takeover, and some are just waiting for direction. That's when Bruce returns. He's respected but feared because they thought he was dead for a long time, they almost look at him as immortal (like ra's).
He takes in Dick Grayson who's parents were killed by Tony Zucco at a circus. Bruce dubs him Robin in honour of John Blake who was the first man who took Batmans torch. Penguin has taken over as the Mayor, Black Mask has infiltrated a lot of key businesses, it's just mayhem now. Bruce has to lead his men so they can change it around, and prepare for a new young generation at the same time. By the end, all crimelords are wiped out and Batmans symbol has spread and infiltrated businesses, other political movements, the police. There's 1 in each field, to make sure that it always stays positive and the people are always in charge and able to fight off any crime. Just like the League of Shadows had their people planted in unlikely positions, it's the same here.
Each of them may have different identities, even if there's not an actual Batman around. If there is at this point, it would be Terry McGinnis. Tim Drake could be a cop. This part could be stupid so toss that out if u like, but it's just me brainstorming. They're all traced back to the school of orphaned children that's located in Wayne Manor.
So i took your ideas lol and went a bit crazy. You can even forget all that crap, and just go with the basics (your idea of a trilogy minus all the details i added) and it would be pretty cool. Even as a graphic novel or on paper only.