They almost surely would not be married if Diana were still alive. Charles, as the Heir Apparent and a man who knows that his popularity is extremely iffy, would absolutely not have gone against the CofE's position on the Sovereign remarrying while an ex-spouse was still alive, and especially not if she were still single. He would have hated it, and I'm sure that he and Camilla would have arrived at a "discreet domestic arrangement" for the duration of Diana's life, but there is no way that the Queen would have given him permission to marry under those circumstances.
Also, FWIW, there is precedent for someone being Princess of Wales in her own right, though I've never been able to determine exactly why, since up until the recent repeal of the primogeniture laws, daughters of living Kings normally were never considered the Heir Apparent, because there was always the chance that their father might yet have a boy child. The daughter of George IV was Charlotte, Princess of Wales, whose mother, Caroline of Brunswick, also held that title from 1795-1820. Technically, the mother was THE Princess of Wales, and the daughter was Charlotte, Princess of Wales in court documents; there appears to be a subtle difference inherant in that wording. Charlotte, Princess of Wales married Prince Leopold of Belgium, but died in childbirth with her stillborn first child when she was only 21, in 1817. At that point her father was still the Prince of Wales. (As far as I can determine, Charlotte appears to have first been referred to by the title "Charlotte, Princess of Wales" when her father was appointed Regent in 1811; she was 6 years old then, and her parents were completely estranged, as they would remain until Princess Caroline's death, three years after that of her daughter Charlotte.)