Doc Brown from 1985 goes to 1885 not the Doc Brown from 1955.
The older doc went back to 1885.....
Timeline to follow.....
1955 Doc Brown hits his head creates idea for the flux compositor, sends Marty back to the future.
1985 Doc Brown steals nuclear thingy from the people trying to kill him and builds time machine.
1985 Doc Brown doesn't die has vest on (Marty left note with him in 1955 about this)
1985ish or there about ... Doc Brown travels to future 2015 discovers Marty's son in trouble
Course of part II is Marty's and Doc Brown go to 2015 stop Marty's son from getting in trouble...
1985 - alternate universe they return to discover biff traveled to 1955....
1985 - Doc Brown and Marty return to 1955
1955 - car with doc brown is struck by lighting just before returning to their real time in 1985
1885 - Doc brown get shoot (later changed by Marty)