Question: How is the namesake of The Mountbatten Institute related to Elizabeth II?

Context:
Sapphire Jubilee of Queen Elizabeth II
On 6 February 2017, the Sapphire Jubilee of Queen Elizabeth II, marking sixty-five years of her reign, occurred.
 The longest-reigning monarch in British history, Queen Elizabeth II was the first British monarch to have a sapphire jubilee.
 This Jubilee featured blue stamps from the Royal Mail, commemorative coins from the Royal Mint, and a reissue of an official 2014 portrait of Queen Elizabeth II by David Bailey.
 In this official portrait the Queen wears sapphire jewellery which she received as a wedding present from her father.
 The Jubilee also involved a gun salute at the Tower of London, a gun salute in Green Park, gun salutes in several other places around the United Kingdom, and the ringing of the bells in Westminster Abbey.
 Theresa May, the Prime Minister of the United Kingdom, congratulated Queen Elizabeth II in regard to the occasion, saying in part, "I know the nation will join with me today in celebrating and giving thanks for the lifetime of service Her Majesty the Queen has given to our country and to the Commonwealth."
Edward Iwi
Edward Frank Iwi (28 November 19046 June 1966) was an English lawyer who was best known as an amateur constitutional expert.
 Many of his opinions, while initially dismissed by the establishment, proved to be correct and caused official policy to be changed.
 Most notable was his advocacy for the Royal Family to adopt Prince Philip's surname of Mountbatten in lieu of Windsor, in order that any Royal children born after Queen Elizabeth II's accession in 1952 would not wear what he called "the Badge of Bastardy".
Queen Elizabeth II Silver Jubilee Medal
The Queen Elizabeth II Silver Jubilee Medal (French: "Médaille du jubilé de la reine Élisabeth II" ) was a commemorative medal created in 1977 to mark the twenty-fifth anniversary of Elizabeth II's accession in the United Kingdom, Canada, Australia, and New Zealand.
 The medal was physically identical in all realms where it was awarded, save for Canada, where it contained unique elements.
 As an internationally distributed award, the Queen Elizabeth II Silver Jubilee Medal holds a different place in each country's order of precedence for honours.
Monarchy of Fiji
The monarchy of Fiji arose in the mid-nineteenth century when native ruler Seru Epenisa Cakobau consolidated control of the Fijian Islands and declared himself King or paramount chief of Fiji (Fijian: "Tui Viti" ).
 In 1874, he voluntarily ceded sovereignty of the islands to Britain, which made Fiji a Crown colony within the British Empire.
 After nearly a century of British rule, Fiji became a Commonwealth realm, an independent sovereign state within the Commonwealth of Nations with Elizabeth II as head of state.
 After a second military coup in 1987, Fiji became a republic, and the monarchy was ended.
 Nevertheless, the Great Council of Chiefs recognised Elizabeth II as "Tui Viti" or the traditional Queen of Fiji, but the position is not one of a constitutional, or otherwise legal nature.
 The Great Council of Chiefs was disestablished in 2012 by decree.
 Elizabeth II does not use the title, and the Fijian government does not recognise it.
Wedding dress of Princess Elizabeth
The wedding dress of Princess Elizabeth was worn by the future Queen Elizabeth II at her wedding to Philip Mountbatten, Duke of Edinburgh on 20 November 1947 in Westminster Abbey.
 Given the rationing of clothing at the time, she still had to purchase the material using ration coupons.
 The dress was designed by Norman Hartnell.
 Hartnell's signature was said to be embroidery, and he enjoyed "working with soft, floating fabrics, particularly tulle and chiffon, and with plain, lustrous silks".
 The dress was made of soft Damascus Prokar, with a high neckline, tailored bodice and a short train.
Earl of Merioneth
The title Earl of Merioneth was created in the Peerage of the United Kingdom in 1947 along with the Dukedom of Edinburgh and the Barony of Greenwich for Philip Mountbatten, R.N. (formerly Prince Philip of Greece and Denmark), the soon-to-be-husband of Princess Elizabeth (now Queen Elizabeth II).
Jubilee Gardens, Lambeth
Jubilee Gardens is a public park on the South Bank in the London Borough of Lambeth.
 Created in 1977 to mark the Silver Jubilee of Elizabeth II, the site was formerly used for the Dome of Discovery and the adjacent Skylon during the Festival of Britain in 1951.
 A multimillion-pound redevelopment of the park was completed in May 2012, just before the Diamond Jubilee of Elizabeth II and the 2012 Summer Olympics, in order to transform it from a state of grassland to a mature looking park with trees and hills.
 Queen Elizabeth II reopened the gardens in October 2012.
Queen Elizabeth II Golden Jubilee Medal
The Queen Elizabeth II Golden Jubilee Medal (French: "Médaille du jubilé de la Reine Elizabeth II" ) or the Queen's Golden Jubilee Medal was a commemorative medal created in 2002 to mark the fiftieth anniversary of Elizabeth II's accession.
 The Queen Elizabeth II Golden Jubilee Medal was awarded in Canada to nominees who contributed to public life.
 The Queen's Golden Jubilee Medal was awarded to active personnel in the British Armed Forces and Emergency Personnel who had completed 5 years of qualifying service.
Mountbatten Institute
The Mountbatten Institute (formerly known as the Mountbatten Internship Programme) is an organization based in New York and London dedicated to fostering work experience and cultural exchange by placing international graduate students abroad to earn postgraduate certificates and degrees.
 Named in honour of Louis Mountbatten, 1st Earl Mountbatten of Burma and benefacted by his eldest daughter Patricia, 2nd Countess Mountbatten, the organization was founded in 1984.
Louis Mountbatten, 1st Earl Mountbatten of Burma
Admiral of the Fleet Louis Francis Albert Victor Nicholas Mountbatten, 1st Earl Mountbatten of Burma, (born Prince Louis of Battenberg; 25 June 1900 – 27 August 1979) was a British naval officer and statesman, an uncle of Prince Philip, Duke of Edinburgh, and second cousin once removed of Elizabeth II.
 During the Second World War, he was Supreme Allied Commander, South East Asia Command (1943–46).
 He was the last Viceroy of India (1947) and the first Governor-General of independent India (1947–48).

Answer: second cousin once removed