I came across this blog by Phil Volk (aka "Fang"), the bassist who replaced Randy in the Stone Canyon Band. It's somewhat of a rambling diatribe against Rick Nelson, but it does give a glimpse into Mr. Nelson's personality and traveling on the road with him. I've wondered about the dispute between him and Randy. From what I've read, Randy voluntarily left the gig on his own, but according to "Fang" this wasn't the case.

[Nelson] mentioned that he was really impressed with my ability to sing difficult songs and play complicated bass lines at the same time. I was very flattered with his comments, but I probably didn't realize that he might have been setting the ground work for replacing his bass player in the Stone Canyon Band and winning me over to his camp, which eventually happened about a year and a half later at the end of December 1969. Rick's bass player at the time was quite a talent in his own right, none other than Randy Miesner, who went from Ricky Nelson to the Eagles. Apparently, Rick let Randy go because of some personality clashes they were having, but it seemed to work out well for Randy, because shortly after that the Eagles began their meteoric rise to superstardom. Unfortunately, Randy only lasted a few years with the Eagles and eventually went off on his own to pursue a solo recording career.
(my emphasis)

Interestingly enough, Mr. Volk had his own run-ins with Rick, and only lasted 7 months with him, despite Rick's admiration of his bass playing (Rick initially thought it would be impossible to replace Randy).

http://www.philfangvolk.com/rickynelson.html