Question: During what forced relocation of Native American nations from their ancestral homelands in the Southeastern United States, did the family of Charles Thompson move to Oklahoma?

Context paragraphs:
Trail of Tears (disambiguation): Trail of Tears was a series of forced relocations of Native American nations from their ancestral homelands in the Southeastern United States following the passage of the Indian Removal Act of 1830.

Cherokee removal: Cherokee removal, part of the Trail of Tears, refers to the forced relocation between 1836 and 1839 of the Cherokee Nation from their lands in Georgia, South Carolina, North Carolina, Tennessee, Texas, and Alabama to the Indian Territory (present day Oklahoma) in the then Western United States, and the resultant deaths along the way and at the end of the movement of an estimated 4000 Cherokee.

Piney, Oklahoma: Piney is a census-designated place (CDP) in Adair County, Oklahoma, United States.  The population was 115 at the 2010 census.  Piney was the "head town" of the first wave of relocated Cherokee people (the "Old Settlers") who relocated there from their ancestral homelands in the southeastern United States.

Barboncito: Barboncito (1821–1871) was a famous Navajo political and spiritual leader.  His name means bearded in Spanish ( Barbon = beard/facial hair and cito= conjucated to add a little flare).  He also was known as Hástiin Dághá (Man with the Whiskers), Hastiin Daagi , Bistłahałání (The Orator), and Hózhǫ́ǫ́jí Naatʼááh (Blessing Speaker).  Barboncito was born into the "Ma'íí deeshgíízhiníí" (Coyote Pass People) clan at Cañon de Chelly in 1820 and was a brother to Delgadito.  He was a signatory of several treaties between the United States and Navajos, including the Doniphan Treaty of 1846 (Also known as the Bear Springs Treaty), which was an attempt to establish peace between the Navajo and whites during the Mexican War.  This treaty proved to be unsuccessful, as not all of the Navajo Chiefs were willing to become signatory to it.  This would later lead to armed rebellion against the United States where Barboncito worked together with another Navajo, Manuelito, in order to try and stop the forced relocation of Navajo tribe members to Bosque Redando.  Barboncito was the Head Chief of the Navajo when the Bosque Redando Treaty of 1868 was signed.  This treaty contained articles which would end hostilities between the United States and the Navajo people, as well as allowing them to return to their ancestral land at Cañon de Chelly in Arizona and having a reservation established there.  The impact of this aspect of the treaty was the end of the Long Walk of the Navajo which had claimed the lives of thousands of Navajo people.  Of all the Navajos of his time, Barboncito is probably most responsible for the long-term success of the Navajo culture and relations with non-Navajos.  As well as being established as a skillful negotiator and leader of the Navajo people.  Shortly after the enactment of the Bosque Redando Treaty, Barboncito died in 1871 at Cañon de Chelly.

Trail of Tears: The Trail of Tears was a series of forced removals of Native American nations from their ancestral homelands in the Southeastern United States to an area west of the Mississippi River that had been designated as Indian Territory.  The forced relocations were carried out by various government authorities following the passage of the Indian Removal Act in 1830.  The relocated people suffered from exposure, disease, and starvation while en route, and more than four thousand died before reaching their various destinations.  The removal included members of the Cherokee, Muscogee (Creek), Seminole, Chickasaw, and Choctaw nations.  The phrase "Trail of Tears" originated from a description of the removal of the Cherokee Nation in 1838.

War Relocation Authority: The War Relocation Authority (WRA) was a United States government agency established to handle the internment, i.e. forced relocation and detention, of Japanese Americans during World War II.  It also operated the Fort Ontario Emergency Refugee Shelter in Oswego, New York, which was the only refugee camp set up in the United States for refugees from Europe.

Charles Thompson (Cherokee chief): Charles Thompson (Utselata, ᎤᏤᎳᏔ also ᎤᏤᎴᏛ in Cherokee) was born to a full-blood Cherokee father and a European-American mother in the Southeastern United States.  According to one writer, the mother had been kidnapped at a young age and raised by Cherokees.  She never learned the identities of her real parents nor when or where she was born.  As a result, she did not speak English and could communicate only in Cherokee.  The family migrated west to Indian Territory during the Trail of Tears, and settled near the present-day site of Lake Spavinaw, in what is now Delaware County, Oklahoma.

Thayer Scudder: Thayer Scudder (born 1930, New Haven, Connecticut), an American social anthropologist, is an Anthropology Professor Emeritus at the California Institute of Technology.  Educated at Harvard University (AB 1952, PhD 1960), he did a postdoctorate in African Studies, Anthropology and Ecology at the London School of Economics, followed by positions with the Rhodes-Livingston Institute for Social Research in Northern Rhodesia 1956-1957 and again in 1962-1963, and a post at the American University in Cairo in 1961-1962.  He joined the Caltech faculty in that year.  His work on socioeconomic issues and infrastructure development associated with river basin development, forced relocation, and refugee reintegration has made him a world leader in these fields.  Large dams are one of the world’s most controversial, divisive and expensive development issues, and Scudder is the world's leading expert on dams and relocation effects.  His 2005 book "The Future of Large Dams" covers aspects of large dams and development including economics, politics, environmental risk, energy, agriculture, and human displacement and resettlement.  He has undertaken studies on sustainable resource use in Africa, India, Nepal, Jordan, Indonesia, Malaysia, the Philippines, Sri Lanka, and the United States, and served on a number of independent review panels for dam projects in Africa and Asia.  He is a former commissioner on the World Commission on Dams.

Executive Order 9102: Executive Order 9102 is a United States presidential executive order ordering the creation of the War Relocation Authority (WRA), the US civilian agency responsible for the forced relocation and internment of Japanese-Americans during World War II.  The executive order was signed by President Franklin Roosevelt on March 18, 1942, and it officially expired on June 30, 1946.  The Director reported directly to the president of the United States.

Indian removal: Indian removal was a policy of the United States government in the 19th century whereby Native Americans were forcibly removed from their ancestral homelands in the eastern United States to lands west of the Mississippi River, thereafter known as Indian Territory.  In a matter that remains one of debate by scholars, description of the policy—which clearly contributed to devastation in numbers, freedom and prosperity for those displaced—is sometimes elevated to being one of long-term genocide of Native Americans, in any case, a consequence of actions first by European settlers to North America in the colonial period, then by the United States government and its citizens until the mid-20th century.  The policy traced its direct origins to the administration of James Monroe, though it addressed conflicts between European Americans and Native Americans that had been occurring since the 17th century, and were escalating into the early 19th century as white settlers were continually pushing westward.  The Indian Removal Act was the key law that forced the removal of the Indians, and was signed into law by President Andrew Jackson on May 28, 1830.

Supporting paragraphs: Charles Thompson (Cherokee chief) Trail of Tears
Answer: The Trail of Tears