When I had a puppy, Athena, with Titan when he was 2 years, and Athena was a weeee 12 weeks
I did a little of independence and a little together. Honestly most was together. Titan knows "go potty" so in the mornings, I would tell him to "go potty" and Athena would be on a leash and told to "go potty" as well. Potty breaks in the afternoon went the same way, as well as in the evenings when I was home from work.
Feedings were done at the same time. Monitored but in the same room and same time. Training was done both ways. Some days when I didn't have a lot of time. I would take them both out. This was Titan's time to work on his "down, stay" Which was pretty solid anyways. I would do the usual "sit, down, here" quickly with both. Take a break and then out Titan in a "down, stay" far enough away that he wasn't a distraction, yet close enough to toss a treat to him periodically. Athena and I would work on everything for a few minutes while Titan did his "stay" and then at the end, I would bring them together for a final "good job!" command and treat. I liekd the idea of training Titan's "stay" at the same time. It was like killing 2 birds with one stone, especially if I was running short on time. Then, always, play time. The only true seperation they got would be while I was at work or at night time while we slept. Athena was in her crate and Titan was allowed to roam the house. At night, Athena was crated downstairs and Titan in my room.
Oh and professional training. I took Athena to puppy classes and Titan to different OB classes. They were one after the other so it made it easy. Drove to the facility, left one in my car during the first class, then a swap. It was winter months, car stayed cool, don't worry! That was always seperate though... the professional training.
It was a little more work, having sometimes to do training seperately and playtime seperately, but mostly it wasn't too different
They were both very independent and didn't need eachother really. Both were more interested in what I was doing, and what I wanted them to do than eachother.. though they played together quite a bit after a while.