Article 130 defines Public Transport and Aerial Work. If a flight is remunerated but does not meet the Public Transport criteria then it is Aerial Work.
Article 29 permits a qualified person to instruct (the licence privileges Schedule 8 will dictate if the holder can be remunerated)
By deduction, if a flight is not public transport but the flight is remunerated, then it must be aerial work and no AOC is required.
Art 101 then lays down the requirement to conduct flying training from a licenced aerodrome.
Assuming that all you do is give instruction, there is no further limitation on where you go so long as the airfield is licenced. There is nothing to say that the student cannot get out at a mid point however, who pays for the return flight? If payment were made then the flight would ammount to public transport for the first leg.
The carriage of persons in the back is not illegal so long as there is no payment for the purpose of the flight. i.e. the only payment is by the student for aircraft hire and instruction. Such a person could get out at a mid point without affecting the status of a flight.
The question is then what is Instruction? Clearly, if the "student" is in the process of qualifying for a licence or rating it would be reasonably easy to authenticate. If there was no tenuous connection, it might be more difficult to establish.