Question: Magnus III of Mecklenburg-Schwerin married the daughter of this monarch who reigned over which two countries?

Context paragraphs:
Magnus Barefoot: Magnus Olafsson (Old Norse: "Magnús Óláfsson", Norwegian: "Magnus Olavsson"; 1073 – 24 August 1103), better known as Magnus Barefoot (Old Norse: "Magnús berfœttr", Norwegian: "Magnus Berrføtt"), was King of Norway (as Magnus III) from 1093 until his death in 1103.  His reign was marked by aggressive military campaigns and conquest, particularly in the Norse-dominated parts of the British Isles and Ireland, where he extended his rule to the Kingdom of the Isles and Dublin.

Tora Magnusdatter: Tora Magnusdatter ("Þóra Magnúsdóttir") (born c. 1100) was a daughter of King Magnus III of Norway ("Magnus 3 Olavsson Berrføtt").

Loftur Sæmundsson: Loftur Sæmundsson (died 1163 ) was a chieftain of Oddi at Rangárvellir in the south part of Iceland.  He was a member of the Oddaverjar family clan and was the son of Sæmundur fróði who had established a school at Oddi.  He was married to Tora Magnusdatter ("Þóra Magnúsdóttir"), daughter of king Magnus III of Norway ("Magnus Berrføtt").  Loftur was the father of Jón Loftsson ("Jon Loptsson") who adopted Snorri Sturluson.

Magnus III of Mecklenburg-Schwerin: Magnus III of Mecklenburg (July 4, 1509 in Stargard – January 28, 1550 in Bützow) was a member of the House of Mecklenburg who was the first Lutheran administrator of the Prince-Bishopric of Schwerin, nevertheless referred to as prince-bishop.  He was the son of Henry V, Duke of Mecklenburg and Ursula of Brandenburg.  He was elected bishop in 1516, but due to his minority and lack of papal confirmation, he only began ruling as an administrator in 1532.  He introduced the Reformation the next year.  He married Elizabeth daughter of Frederick I of Denmark and Sophie of Pomerania.  They had no children.

France–United Kingdom relations: France–United Kingdom relations are the relations between the governments of the French Republic and the United Kingdom of Great Britain and Northern Ireland (UK).  The historical ties between the two countries are long and complex, including conquest, wars, and alliances at various points in history.  The Roman era saw both areas, except Scotland and Northern Ireland, conquered by Rome, whose fortifications exist in both countries to this day, and whose writing system introduced a common alphabet to both areas; however, the language barrier remained.  The Norman conquest of England in 1066 decisively shaped English history, as well as the English language.  In the medieval period, the countries were often bitter enemies, with both nations' monarchs claiming control over France.  The Hundred Years' War stretched from 1337 to 1453 resulting in French victory.  Britain and France fought a series of five major wars , culminating in the Coalition victory over Napoleon in 1815.  After that there were some tensions, but peace generally prevailed and as the 19th century progressed, the relationship became better.  Closer ties between the two began with the 1904 Entente cordiale, particularly via the alliances in World War I and World War II, wherein both countries fought against Germany, and in the latter conflict British armies helped to liberate occupied France from the Nazis.  Both nations opposed the Soviet Union during the Cold War and were founding members of NATO.  In recent years the two countries have experienced a quite close relationship, especially on defence and foreign policy issues; the two countries tend, however, to disagree on a range of other matters, most notably the European Union.  The British press relishes the chance to refer to France and Britain as "historic rivals" or emphasize the perceived ever-lasting competition that still opposes the two countries.

Frederick I of Denmark: Frederick I (7 October 1471 – 10 April 1533) was the King of Denmark and Norway.  His name is also spelled "Friedrich" in German, "Frederik" in Danish and Norwegian and "Fredrik" in Swedish.  He was the penultimate Roman Catholic monarch to reign over Denmark, when subsequent monarchs embraced Lutheranism after the Protestant Reformation.  As King of Norway, Frederick is most remarkable in never having visited the country and was never being crowned King of Norway.  Therefore he was styled "King of Denmark, the Vends and the Goths, elected King of Norway".

Magnus III of Sweden: Magnus III (Swedish: "Magnus Birgersson/Magnus Ladulås" ; 1240 – 18 December 1290) was King of Sweden from 1275 until his death in 1290.

Battle of Hova: The Battle of Hova was fought in Hova, Sweden on 14 June 1275 between peasants commanded by Valdemar of Sweden and Danish cavalry commanded by Magnus III of Sweden and his brother Erik.  The result was that Valdemar had to flee to Norway and Magnus became king of Sweden as Magnus III.  It was a part of the war against Valdemar Birgersson which was a conflict between Magnus III of Sweden and Valdemar Birgersson.  Magnus was supported by the Danish crown with at least a 100 men (source is unsure).

Antonia Pilars de Pilar: Antonia Baronin Pilars de Pilar, née "Antonia Gabriele Marie Josefa Huberta Elisabeth Maximiliane Freiin von Oer-Egelborg" (*10 April 1872 in Birstein; † 7 February 1946 in Störmede) was from 1894 to 1898 court lady of the duchess Marie of Mecklenburg-Schwerin née Princess Marie of Windisch-Graetz and from 1911 to 1944 courtlady of Marie's daughter, the Duchess Marie Antoinette of Mecklenburg-Schwerin.  Antonia married Polish poet Ladislaus Baron Pilars de Pilar.  They had 3 Children: Eduard (1899–1971), Antoinette (1901–1989) and Gabriel (1904–1978).  Antonia was the daughter of Friedrich Freiherr von Oer-Egelborg (1842–1896), chamberlain of Charles II.  prince of Isenburg and Gabriele née Countess Khuen von Belasi (1841–1923).  Her son Gabriel married in 1935 Anna, Countess von Stubenberg.

Norman invasion of Wales: The Norman invasion of Wales began shortly after the Norman conquest of England under William the Conqueror, who believed England to be his birthright.  Initially (1067–1081), the invasion of Wales was not undertaken with the fervor and purpose of the invasion of England.  However, a much stronger Norman invasion began in 1081 and by 1094 most of Wales was under the control of William's eldest son, King William II of England.  The Welsh greatly disliked the "gratuitously cruel" Normans and by 1101 had regained control of the greater part of their country under the long reign of King Gruffudd ap Cynan, who had been imprisoned by the Normans for twelve years before his escape.  Gruffudd had some indirect help from King Magnus III of Norway (Magnus Barefoot) who attacked the Normans briefly off the Isle of Anglesey in northwest Wales near Ynys Seiriol, killing Hugh of Montgomery, 2nd Earl of Shrewsbury and leaving the Normans depleted and demoralized.  Magnus went on to take the Orkney Islands, the Hebrides, and the Isle of Man, islands north of Wales and west and north of Scotland and England, in 1098.

Supporting paragraphs: Magnus III of Mecklenburg-Schwerin Frederick I of Denmark
Answer: Denmark and Norway