I know =P But I enjoy linguistics, so I'm kind of geeky in the subject =P
Well, you see. I'm mexican, so I speak spanish; my language's phonetics are more "opened" than english's, we gesticulate more; and english has too many "intermedium" sounds, like "tear", "read", "create"; so I DO HAVE an accent in a way. The "R" sound from english isn't in spanish, and the "hard R" sound in spanish isn't in english; but when I talk in english I pronounce the "R" the "english way", the movies I talked about are 50 years old, when studying abroad or learning another language wasn't really a priority, and people didn't bother trying to pronounce things correctly. So I think there's nothing wrong with you having an accent, but when it is about OFFICIAL pronunciation, you must do it correctly =P
About your problem pronouncing the "hard R", don't be too harsh with yourself, it is hard for somebody who has never pronounced it before, let's see if this one works for you... put your tongue just like you would do when pronouncing an english R, now in that position stick it to your palate and try to get some air to go in between your tongue and palate, but don't let your tongue unstick too much from the palate, you will eventually make a sound similar to a cat's purring, go on and let a little more air get through and, with a little more practice, you'll get the sound