I don't add an "r" at the end of "idea". You may be thinking of the use of the tongue rather than a stop to join words like "idea of"; this I do - but it is actively avoided when singing, because it becomes ugly and slovenly-sounding when drawn out. But I would also not voice the "r" at the end of "father", though again one might appear in a phrase like "father of".
As for RP, it's not fixed. I would describe it as the speech of a well-educated person of the home counties (the area around London), and I would have to admit that this is commonly taken to mean more particularly those who went to a public school (i.e. a private one) such as Winchester or Eton (or in my case The King's School, Canterbury); but this does change with time, and so RP now is not the same as the RP that was spoken by King George V, for instance.