It would probably be cheapest to get Advance tickets, one (or more) for each leg. As you say you intend to book assistance, I don't suppose that she would get much benefit from a flexible ticket anyway. I would simply see what TrainSplit suggests, it will usually come up with a good suggestion.
In terms of the route, for Stoke-Leeds you're best off changing at Manchester Piccadilly - there are no stairs to negotiate if you get trains that terminate and start in the 'main shed'.
During the current timetable, if you're travelling off-peak on a weekday there is a decent 12 minute connection off the XC service onto a Hull service.
For Leeds-Blackpool North, there is a direct hourly service via Bradford and Burnley, and there are lifts at the station (most such trains leave from platforms accessed via the footbridge from the main entrance).
For Blackpool North-Stoke, the easiest route is probably to take a Hazel Grove service and change at Stockport - that would be a level, cross-platform change.
All of the stations in question are staffed so assistance shouldn't be a problem.