No, you are wrong. Charles was never The Prince Charles because that is a title and he has never had that title.
And Andrew and Edward (and all other princes who receive royal dukedoms or other titles) cease being Prince First Name of Wherever or The Prince First Name when they receive their new titles.
Names and titles are different things. Of course The Prince of Wales is Prince Charles Philip Arthur George. That is his name and his rank. But his title is HRH The Prince of Wales. His wife takes his rank and his title. She does not take his name. Same with all the other princes.
Like all the children of the monarch he has the title of The Prince Charles. He has other titles as well but he also has that one - and uses it in Scotland.
You may continue to believe what you like but you are wrong.
All children of the monarch are The Prince/Princess xxx. They may then add other titles but that basic title is theirs as well. As he was born a Prince Charles has always held the title of prince. When his mother became Queen, along with adding Duke of Cornwall etc he added the word 'The' in front of the title Prince - simply to show that he was the child of the monarch.
Charles has a lot of titles that he doesn't use - that doesn't mean he doesn't have them though. No Prince loses the title of Prince when they gain a title - they add the title to the one of Prince e.g. William is still Prince William but he is also The Duke of Cambridge, Andrew is still The Prince Andrew but he is also The Duke of York - you don't lose titles.
How is that too hard to understand?
If you had read post # 938 in this thread you would even see that The Court Circular - the official listing of the activities of the royal family refers to Charles as 'HRH The Prince Charles, Duke of Rothesay' when he is in Scotland. Look at the entries here for the 14th, 18th and 27th April as they all refer to The Prince Charles Duke of Rothesay -
http://www.royal.gov.uk/LatestNewsandDiary/CourtCircular/Todaysevents.aspx e.g.
27th April 2011
CLARENCE HOUSE:
The Prince Charles, Duke of Rothesay, President, the Great Steward of Scotland's Dumfries House Trust, this afternoon attended a Reception at Dumfries House, Cumnock, Ayrshire.
His Royal Highness, President, the Great Steward of Scotland's Dumfries House Trust, this evening gave a Dinner at Dumfries House
As the above comes from the official website of the British Monarchy I will assume that they know the correct titles of the members of the family and that site calls him 'The Prince Charles' so he obviously holds that title.
Wives in Britain take all the titles etc of their husband's and so on marriage the wife of a Prince becomes a Princess but as she wasn't born a Princess she isn't Princess own name but Princess husband's name e.g. Princess Michael of Kent. Because Michael has no other title his wife takes his name when using a title at all. As the other men all have titles the formal way to refer to them is by their title but their wives are still princesses but as they can't be Princess Camilla as Camilla wasn't born a Princess she would have to be Princess Charles - taking the feminine form of her husband's title of prince just as she takes the feminine form of his title of Duke of Cornwall (or any wife is formally Mrs John Smith on marriage to Mr John Smith not Mrs Jane Smith e.g. Carole Middleton at Ascot last week - her name tag had her as Mrs Michael Middleton - the feminine form of her husband name and title.)