The fast Edinburgh to Glasgow services don’t call at Edinburgh Park, so using a normal day return, would I need to change at somewhere like Polmont or are you allowed to double back and change at either Haymarket or Waverley?
The ‘technical’ answer is: no, you may not travel via Haymarket or Waverley. [EDIT: Under the standard routeing guide procedure. There is a separate local easement - see later in the thread.]
It is possible to generate itineraries (such as on the ScotRail app) if you specify the relevant station as a via point. Provided that you purchase the ticket by that means and follow said itinerary then you should be fine.
However, your journey will normally be quicker changing at Polmont (roughly 5mins wait to Glasgow and 10-15mins on the way back).
Similarly, the through trains between Edinburgh Park and Queen Street Low Level take roughly the same time as changing at Haymarket or Waverley because of how the connections fall.