Obviously, his personal way of addressing her wont change.Yeps. Unless (let's say for example) she married Hasnat Khan. Then she'd be Mrs. Hasnat Khan and lose the courtesy styling as an ex-wife of a peer.
William's addressing her as "mum" would never change. Ever.
But if she had married Hasnat Khan or Oliver Hoare or whoever, she woudl be Lady Diana Khan/Hoare or whatever her husband's surname was. Her Lady Diana courtesy title would not disappear and she could still use it if she married an untitled man. of course if she married a peer she would take HIS title.
I think that had she lived, it would have been better to give her a peerage in her own right.. to take away the "Princess" problem if C remarried..
If Diana was say Countess of Brington.. (is that the name of hte village near to her home?) she would have a settled title in her own right. if she remarried and had more children- they would be Lady Mary X or The Hon Christoper X..I think it woudl have satisfied her to have a title that was hers, and not dependent on being Charles' ex wife or William's mother.