Is the following better than what you have found:
Rishton - Kiveton Park £23.50 via Burnley anytime day return
Kiveton Park - Whitwell £4.30 offpeak day return
Whitwell - Mansfield £5.30 offpeak day return
Total: £33.10
Itinerary:
Rishton 0836 - Accrington 0842
Accrington 0903 - Leeds 1023
Leeds 1040 - Sheffield 1137
Sheffield 1144 - Worksop 1213
Worksop 1238 - Mansfield 1310
Mansfield 1657 - Worksop 1733
Worksop 1810 - Sheffield 1835
Sheffield 1850 - Leeds 1951
Leeds 2008 - Accrington 2120
Accrington 2159 - Rishton 2204
I should add that the suggested ticket combination forces you to travel via Worksop (as well as via Burnley): Kiveton Park, and Whitwell, are stations either side of Worksop on the suggested itinerary. And it goes without saying that with the suggested combination you would require you to take trains that call at Kiveton Park and Whitwell, but the trains in the suggested itinerary do satisfy this requirement.
