Perhaps what keeps Harry and Chelsy together is that understanding about family connection and how the public prejudges him based on that family connection. As a member of RF, there will always be people trying to gain access to him and profit from that access. Harry strikes me as less guarded than William, but it must be in the back of his mind. In the press, Harry has been cast as the wild "spare" to the angelic heir. His partying and run-in with photographers gave the public further evidence of that impression. He gave a couple scripted interviews which helped for awhile until the next incident.
As for Chelsy, even less is known besides "accroding to friends" sort of news. Most children wouldn't be aware of everyone their parents work with, but all the press about her father's business associates can't be lost on her. Most of the chatter about her unsuitability, even as Harry's girlfriend, goes back to her father's association. Mr Davy could very well be sympathetic or even supportive of Mugabe. However, as far as I can find, there has been no reports of Mr. Davy actually participating in the campaign against white farmers or dissidents instigated by the Mugabe regime. He is condemned as guilty for the regime's repression by association and Chelsy is guilty by blood connection.