It's not uncommon for a small fleck of bone to be pulled off in a dislocated elbow. It is where one of the ligaments attached to the bone. As long as the piece of bone is not so large that it gets trapped in the joint, or causes the joint to be unstable, it is just ignored.
The vast majority of dislocated elbows are stable after reduction. The usual treatment is a sling for just a few days, then range of motion is started. Once the range of motion is pretty good, then strengthening can start.
It is also not uncommon for the patient to lose some range of motion at the extremes of flexion and extension. The functional arc of motion is from about 20 to 120 degrees.
Remember, it took a lot of energy to dislocate an elbow, and the soft tissues around the joint have been damaged. They heal with scar tissue. That scar tissue has to mature. With range of motion and time, most patients can get back to their usual activities. But, it does take effort and time.
Good luck.