Thank you all for the explanations.
Not that I understand nor have retained any of it. ? Methinks all this is on the order of that old stand-by, the 'need-to-know'. I don't really need to know all this so it doesn't stick at all. Of course, it could also be mother-brain in operation. Yes.
Let's imagine that Harry is created Duke of Highgrove, Earl of Balmoral, Baron Enniskillen (to not pick likely contenders) on his wedding day.
During the Queen's reign:
Harry and Meghan will be The Duke and Duchess of Highgrove
As male-line great-grandchildren of the monarch (Elizabeth) their children will not be styled as princess, but as children of a Duke.
So, their eldest son will use Harry's secondary title and will be known as the Earl of Balmoral
Other sons would be: Lord X Mountbatten-Windsor
Daughters would be: Lady X Mountbatten-Windsor
During Charles' reign and afterwards (under the condition that the current Letters' Patent are not somehow changed). Harry and Meghan will remain The Duke and Duchess of Highgrove, but as male-line grandchildren of the (former) monarch (Charles) their children will be styled as princes and princesses 'of Highgrove'.
Harry & Meghan's male-line grandchildren will be male-line great-grandchildren of a monarch (Charles), so the above applies again. The eldest son of their eldest son (the line in which the title will be passed on) will be the Earl of Balmoral - if he would have a son, the eldest son would be known as Baron Enniskillen. All others are Lord/Lady Mountbatten-Windsor. They, however, will never become princes and princesses. Only the title of the heir will change at some point to take over Harry's title as Duke and then the secondary titles also pass down one generation.
H&M's female-line grandchildren will be Miss/Mister 'Surname of their father'.
H&M's eldest son (if they have one) will most likely at some point become HRH The Duke of Highgrove (unless LPs' are changed); his children will be Lord's and Lady's, his male-line grandchildren by his eldest son as well - but by other sons and daughters any grandchildren would just by Miss/Mister Mountbatten-Windsor (for male-line), Surname of their father (for female-line). His eldest son (a great-grandson of Charles) will be known as Earl of Balmoral until he become the Duke of Highgrove - when he takes over the Duke title, he will not be a Royal Highness but a His Grace as the title ceases to be a Royal Dukedom (as we will see in the next decades with the Duke of Kent and Duke of Gloucester titles).
Hmm, don't think it is much clear now, actually. Most important is that:
1) Only children and male-line children of the monarch are prince(ss) with the 'territory' of Harry's Dukedom.
2) Children of titled descendants (who are not prince(sse)s are Lord / Lady Mountbatten-Windsor, except for the direct (male-line heirs) who will use the secondary title(s).
3) The Dukedom ceases to be royal (HRH --> HG; also has implications for order of precedence) when it is passed on to someone who is not a son or a male-line grandson of a monarch.
