Here's a link (don't know how reliable,) stating
"The personal jewels of Lady Diana are noted as such. If the jewels were not loaned to her by the Queen, they are the property of Lady Diana. After her death, they were either sold or put away for her children, Prince William and Prince Harry to inherit. . . []
"Princess Diana was allowed to keep the jewels given by the Queen after her divorce, on condition that they could not be lent or sold. However, after her death the jewels were returned to the Queen."
http://tudorswiki.sho.com/page/Jewellery+of+Today%27s+British+Royalty
I would imagine some sort of similar deal would also be made with Kate, should they break up or divorce. That ring still has the history that it belonged to
Diana, and thus is part of the Royal history. (Plus, it is dear to both William & Harry.) Kate having had it for a while would just be an addendum to the already established history.
I think eventually the ring will become part of the Royal Family jewelry collection. The Crown Jewels are only part of the whole collection. During their
lifetime the Royals get pretty much everything they own, on
loan. This is why the non-Royalists make such a fuss about how much they lavishly have & spend. Even their salaries/duchys are furnished by the British taxpayers. So when they make lavish purchases they are criticized for it, because ultimately it's taxpayers' monies.
The ring is now part of the Royal
history. A history which helps the Royals earn for their keep. Which is why I would think it would go into the Royal Collection. I had to pay admission to see the Crown Jewels & collection, when I went. The Royal Jewelery collection isn't
just the crowns. It's a museum collection, pretty much all the past Royal jewelry. I remember the room clearly as I was exceptionally dazzled by the crowns and the gazillion other jewelry pieces, labeled with their full history and who were the owner(s.) It's a huge museum space. Think of 3 full jewelry stores stacked in and around that room, with the largest, brightest bling imaginable.
Diana had even borrowed a few old pieces from former queens/duchesses and had them reset into more modern settings to wear this lifetime. I remember reading about it when she had them done. They are able to retrace the whole history, like an ancestral tree, of who gave it to who, who next owned it and wore it for what occasion, and so on, until Diana reset the stones. Now, her re-settings are part of the history of those pieces.
Diana's ring would bring in a lot of money for viewers who want to see it. The OP wants to OWN a replica. Case in point. It helps promote more of the Royal Monarchy.