AFAIK if for example Madde marries in she is a Princess of her own right, but a commoner is Princess Henry.
I think they will give him a Dukedom, but their children won´t be Prince and Princesses, like the Gloucesters I guess.
I am not sure if Maddie would be allowed to be Princess Madeline. There are two recent examples.
Prince Philip had to give up his Greek titles. It was his father in law who granted him the title upon marriage, as well as DOE, of Prince of the UK in his own right.
Princess Marina of Greece and Denmark married prince George, Duke of Kent. During his wife, and her early years as a widow, she was HRH The Duchess of Kent. When her son wed, she reverted back to her own personal title of HRH Princess Marina, Dowager Duchess of Kent. But she had permission from the queen to do so, as there was a new Duchess of Kent.
Prince Harry's children would not be title prince or princess, as they gain their titles from their dad. Until Charles becomes king, and Harry's children are the grandchildren of the king, that is. Until set time, they'd be titled as children of the Duke, so Lady/lord, and the heir would have his lesser title.
I hope when succession laws change, some other rules change. Like only male-line grandchildren being HRH, and daughters not getting a dukedome of their own (Anne's husband turned down a title not her). It would be odd if Will has a daughter as his heir, but she gains no dukedome, and her children have no titles but a younger brother's children do.