You probably won't find that sort of detail in the Policy itself. However, it is standard insurance business practice to repair the car to the standard it was before the damage beause of the word 'indemnity'. What this means is that they are obliged to return you to the state you were at BEFORE the damage occurred. i.e. you had an undamaged car with good paintwork. If that hasn't happened then you haven't been indemnified. (This is all linked in with the 'Betterment' thing you mentioned....they can't leave you better off than you were before the damage either)
Anyway, they have made the effort to have the car repaired, but if the work is not satisfactory, then they have to be given another chance to indemnify you properly. This means that they will probably give the paint shop another chance. If you are REALLY unhappy, then insist that you are not willing to let this place touch your car ever again. Not sure is they'll go with that as they have already gone part of the way down the road with this paint shop now and may be obliged to let them sort out their mess.
If after a second bite at the cherry, they paint is still rubbish, then insist on the insurance company taking it ot a paint shop of your choice. Threaten them with going to the Insurance Ombudsman if it all gets sticky. Win or lose, it will cost the insurers about £750 just to go to the Ombudsman, so they'll be keen to avoid that.
I see you're in Bury St Edmunds. You could do alot worse than having it done a Les Bedfords of Reepham Road, Norwich. They are the only authorised Rolls Royce repair shop in the area so the quality is obviously good, and have done a number of Supras over the last couple of years, including both of ours, IanC's, Alex's and recently Digsy's car too.
Don't let go of this. If your not happy that the car is in the condition it was before the damage occurred, then they have a duty to make it so.
Good luck mate!