None are royal. The non-royal peerage title passes on to the eldest son. Prince Michael's children are not royally titled and bear courtesy stylings of Lord or Lady. Younger children of the Kents and Gloucesters are also styled Lord or Lady.
Only the children of a monarch, the grandchildren of the monarch, and the eldest son of the eldest son of the Prince of Wales bear royal status under Letters Patent written by George V:
"... it being Our Royal Will and Pleasure that the grandchildren of the sons of any such Sovereign in the direct male line (save only the eldest living son of the eldest son of the Prince of Wales) shall have and enjoy in all occasions the style and title enjoyed by the children of Dukes of these Our Realms Our Will and Pleasure further is that Our Earl Marshal of England or his deputy for the time being do cause these our Letters Patent or the enrolment thereof to be recorded in Our College of Arms to the end that Our officers of Arms and all others may take due notice thereof. In Witness whereof We have caused these Our Letters to be made Patent Witness Ourself at Westminster the thirtieth day of November in the eighth year of Our reign."
http://www.heraldica.org/topics/britain/prince_highness_docs.htm#1917_2
Under these rules, the Duke of Gloucester's eldest son,(Alexander) Earl of Ulster, becomes Duke of Gloucester when his father dies. Alexander's sisters are given the courtesy styling "Lady." The Lady Davina Windsor (now The Lady Davina Lewis) and The Lady Rose Windsor (The Lady Rose Gilman), and their brother do not carry out official duties and are private citizens.
THe Duke of Kent's eldest son will inherit the dukedom when nis father dies, while others bear courtesy stylings of Lord of Lady.George, Earl of St Andrews, becomes the next duke; Lady Helen Taylor, and Lord Nicholas Windsor have courtesy stylings of younger children of a duke. None of the children carry out official Royal duties.