Yes absolutely, you can always ask the driver to go somewhere different, but they certainly won't always be happy to do this if it isn't convenient for where they need to go next and you are not the direct customer.
I would have thought they could do a return trip if booked in advance (by the TOC). I believe that GTR have an agreement with specific taxi companies for this type of thing, so assume that these jobs count as 'private hire' (that is like a mini-cab) rather than a 'taxi' journey that was 'hailed', even if the vehicle is licenced as a taxi. As an aside, you can even 'private hire' licenced (London) black cabs, as my disabled Father in Law used to do to be conveyed in a wheel chair. TOCs probably don't pay the meter fare, even if the meter is running, but are likely to have previously agreed rates with taxi / mini-cab operators.