Diana was divorced but still known as Princess. Neither Diana or Sarah were HRH after their divorces, but they do have every right to be referred to as Duchess and Princess, just as the Earl Spencer has ex wife called Countess Spencer.
Why should Sarah be singled out and not allowed to be called Duchess, this is a simple right she has as former wife of the Prince.
She is not HRH, but she is still Duchess.

Sarah also went to the US because it was an opportunity for her to pay off her enormous bank debts. after the divorce(which the UK press was on her constantly about.) She did what she needed to do and paid her debts. If she had stayed in the UK and remained in debt, not paying them off, the press would still have complained about her. She did what was best to pay off her enormous bank drafts. The Americans were willing to pay her well, so she took the U.S. contracts and now she is debt free.

update

I inquired a bit, and know why kate was not with william and friends during the week holiday in cornwall … she was at the marketing show (1er of july on wednesday) and on the 3rd she was with friends clubbing at the raffles and we known william was back on duties on the 6th of july (so probably back around the 5th).

I just see Sarah has a true survivor for making out alive from the hole she was in all those years ago. The royals treated her badly and the media got very nasty with her. Even though she has fought her way back to the top and live a much healthier lifestyle, I just find it cold to throw her painful past back into her face. The British press always manages to do that and I hope the British people is not that cold.

Diana was on a path to gaining her life back and looking for more serious causes to support, that all came to an end in Paris.