Judy, morning sun and afternoon shade is especially important in the south - from what I read about Caroline she is pretty forgiving for a rhododendron. The suns rays are strongest between approx 11 - 2, if your site offers some protection during mid day I think it's worth a try.

Mulch the root zone with something organic (those maple leaves run over with a lawnmower would be great if you've kept them) and provide regular water especially the first year while its becoming established. If you are finding evidence of sunburn after your rhododendron is established, they are relatively easy to move and you could find it a new home then if necessary.