I'm sorry that I can't provide a reliable answer, ...
. . . This extended availability is for interchange purposes only . . .
suggests that this is not permitted.
I don't think a definitive answer can be obtained by reading this phrase on its own. The full description of Group Stations is
Some stations are grouped together to improve interchange between trains by offering customers access to a wider choice of train services and station facilities. A customer may travel via any station in such a group, including doubling back, provided that the group is on one of the permitted routes between their origin and destination stations. This extended availability is for interchange purposes only and does not apply where the origin or destination stations are part of a group.
The reference to
interchange purposes only, in my opinion, adds no additional burden for the passenger doubling back within an intermediate Group. If a passenger travelling on a ticket valid for break of journey decides to stop for a meal at an Edinburgh Group station, and prefers a restaurant close to Dalmeny rather than one close to Edinburgh (Waverley), then in my opinion the words on Group stations gives the passenger the right to travel via Dalmeny.
In post #26 I said I didn't know whether it could be permitted to travel through a station more than twice. While stressing heavily that we're all giving opinions and that it's unlikely that we'll ever get a definite ruling, I'm now moving to the view that it probably has to be permitted. Let's continue my scenario ...
When the passenger finishes their meal they may resume their journey. From Dalmeny most (but not quite all) valid journey opportunities involve doubling back within Edinburgh Group at least as far as Haymarket. It would usually be most convenient to change at Haymarket, because most (but not quite all) Edinburgh (Waverley) - Glasgow trains call at Haymarket. But at some times it would be better to change at Edinburgh (Waverley) for Glasgow Central to catch a fast train which does not stop at Haymarket. And if the passenger has difficulty with stairs, it is always necessary to change at Edinburgh (Waverley) because the lifts have not yet been installed or commissioned at Haymarket.
If the passenger doubles back as far as Edinburgh (Waverley), they may or may not pass through Haymarket more than twice because most (but not quite all) Edinburgh (Waverley) - Glasgow trains which do not call at Haymarket pass through that station. A few go via Portobello instead. As far as I can ascertain, the information on which route a particular train will take between adjacent station stops on a particular day is not in the public domain.
When the first Routeing Guide was published in 1996, the Rail Regulator wrote in this
press release that
I am satisfied that the Guide ... will guarantee for the passenger the reasonable routes currently used. I can't believe that the Rail Regulator's current successor for routeing matters, the Secretary of State, would decide that the validity of travelling through a particular sequence of station stops would depend on the precise route travelled for route learning purposes between one station stop and the next, where that route is not made available to the public. For that reason, I have come to the view that it can be permitted to pass through a particular station more than twice on a Permitted Route for a particular journey.
the "for interchange purposes" is probably basically their way of saying you can't break your journey while on the 'doubling back' section.
I don't think so. The only Permitted Route for a South Milford - Church Fenton journey is via Leeds Group. I can see nothing in the Guide which would indicate that break of this journey would be permitted at Micklefield, where doubling back is avoided but there are few facilities in and around the station, but not at the other members of the Group where facilities are greater.
In the Newcastle - Glasgow via Dalmeny example, travel between Newcastle and Dalmeny does not involve doubling back. If resuming this journey after a break at Dalmeny, there is a permitted route to Glasgow Queen Street which does not involve doubling back, but has a service of only 5 trains a week (M-F: 07:14 Kirkcaldy - 07:42 Dalmeny 07:42 - Glasgow Queen Street 08:47). At other times, doubling back is needed to complete the journey, but this is caused by the level of train service provision.