Same with using Leeds to Rotherham via Meadowhall.
Leeds-Rotherham would be fine via Meadowhall if it wasn't for easement 700130. This says:
Customers travelling from Leeds to Rotherham Central, Swinton or Mexborough in possession of tickets routed 'Not Doncaster', may not travel via Meadowhall. This easement applies in both directions.
If you buy a ticket which doesn't meet the three criteria which are listed there, you may be able to travel via Meadowhall.
Although you would think they would put Northern only or not valid via Sheffield on the ticket, rather than not valid via Doncaster which wouldn’t gain you anything as a passenger.
They put "not via Doncaster" on them because someone else sells tickets which
are valid via Doncaster. Neither operator expects people to travel via Sheffield, though.
If going via Doncaster works out for you, there is easement 700507. This says:
Customers travelling from Barnsley, Wombwell, Elsecar and Chapletown to or via Doncaster may double back between Meadowhall and Sheffield. This easement applies in both directions.
Finding a ticket which would be useful in your circumstances may not be straightforward, though.