No, there is no Princess Charles, no Princess Edward and no Princess Richard in the United Kingdom...
The difficulty I am having is with your continued argument that Princes cease to have one title when they gain another. They don't. They add titles but don't give up the ones they already have so:
The Prince Andrew is also The Duke of York and thus his wife was The Princess Andrew AND The Duchess of York
The Prince Charles is also The Prince of Wales, The Duke of Cornwall etc and thus his wives were both The Princess Charles AND the female form of all his other titles.
The Prince Edward is also The Earl of Wessex and so his wife is both The Countess of Wessex AND The Princess Edward
Prince Richard is also The Duke of Gloucester and so his wife is both The Duchess of Gloucester AND Princess Richard
Prince Edward is also The Duke of Kent and his wife is both The Duchess of Kent AND Princess Edward
Sure only Princess Michael uses that designation but that is only because Prince Michael has no other title.
Not hard at all.
The Princes keep all their titles until they either merge with the crown or die.
Thus there is a Princess Charles, two Princess Edwards, Princess Richard and Princess Michael but only one of them has no other title to use and thus uses that one where as the other ladies have other titles to use and do so - Duchess of Cornwall, Countess of Wessex, Duchess of Kent (the other Princess Edward) and Duchess of Gloucester.
You keep making the same claim and simply keep refusing to believe it when you are told the most basic principle - they add the titles to those they already have - they don't lose the title.
Charles didn't stop being Prince Charles when his mother ascended the throne and he became Duke of Cornwall. He added Duke of Cornwall to his title of Prince and also added the designation 'The' as the son of a monarch. Princes Andrew and Edward didn't stop being Princes when they were created Duke of York and Earl of Wessex respectively. Prince Richard of Gloucester and Prince Edward of Kent didn't stop being Princes when they inherited their titles.
They stopped using them but that isn't the same as stopped having them.
The best example would actually be Philip - he had the titles Duke of Edinburgh etc for 10 years before he was actually created' The Prince' Philip - showing the adding of titles - he didn't stop being the Duke of Edinburgh he added The Prince to his titles (he wasn't Prince Philip from 1947 until 1957) - and thus Elizabeth - on top of her titles in her own right could also use The Princess Philip (why she ever would is another matter but she still has that rigth as Philip's wife) Duchess of Edinburgh etc. If holding a title like Duke means that they stop being Princes and thus their wives aren't princess then why take the trouble of issuing LPs to give Philip the title of 'The Prince Philip etc'?
It is simple as you say - you add titles to those you already hold.
The only problem is that your version of what happens in wrong.