My kiddos all had different bedtimes because different schedules for daycare or if they were home with me - but ultimately, they went to bed when really groggy, so it wasn't too hard to just pop them in bed and they konked out at that age. I didn't have your problem. I did not drag out the bedtime routine. It was one board board, a kiss, into bed, lights off. They were asleep within minutes.
Mine did not share rooms at 2. Mine sometimes got up around 6 am at that age. I think that was fairly common if I can recall. They were usually hungry.
As for naps, some of mine gave them up around 2 1/2 or so. Or some did some days, but not others. I didn't have a set routine. I never would have returned them to bed. I don't think any of mine slept in bed for naps at that age. Crashing on the couch, or wherever was more the norm. I was kind of encouraging sleeping at night and just cat napping at that age - so they would drift as needed during the day - and often would with noise going on around the house.
I found then they would sleep very soundly at night.
We also got lots of activity during the day. After dinner (evenings) was gym time at our house. That could mean dad lay on floor and kiddos all piled on top of him - but it meant that they were active rather than watching shows, for part of the evening any how. Or they headed outside for a bit. That seemed to help too.