Ok so you obviously caught East Midlands Trains Liverpool service from Chesterfield in the morning which does indeed reverse at Sheffield and then travels back towards Dore where it take the Hope Valley route through Totley Tunnel and on past Stockport and into Manchester.
Your description of the return journey however makes no sense. If you caught EMT's Norwich service which is the return of the Liverpool that you caught in the morning, then you would have come back the way you went................there is no alternative route.
The only way you could have arrived into Sheffield travelling in a southerly direction would be to have gone from Manchester to Leeds then caught another train from Leeds to Sheffield, if then you say you set off again from Sheffield in a Northerly direction then the only way to do that would be to go via Woodbourn jct , Darnall, Woodhouse jct, Beighton jct past Killamarsh, Renishaw and Barrow Hill to finally arrive at Chesterfield, crossing back onto the main lines at Tapton jct or did you arrive in Chesterfield on the new platform 3? Either way you could not have gone through Bradway Tunnel if you set off North from Sheff'
Hope this clears it up for you,............................................................. but perhaps not!