In her National Catholic Register article about the exhibition on St. Thomas More at the Saint John Paul II National Shrine in Washington, DC, Charlotte Hays notes the source of several of the relics on display:
Several objects in the exhibit were given to the Jesuit college in the 18th century by Jesuit Father Thomas More, the last male descendant of St. Thomas More (More had four children, three daughters and a son). These include an enameled gold crucifix that has three pearls hanging from it and likely contained a relic, now lost, of an earlier saint. Because of the size of the crucifix, it likely sat on More’s desk rather than worn around the neck and likely was on his desk in the Tower of London. A homey gift from Father More was the saint’s reversible nightcap, made with golden thread and gilded spangles. Family history attributed the cap to More’s beloved daughter Meg.
The Center for Thomas More Studies has this resource for the family tree (though not in the form of a family tree) for the More family, based upon a book from Gracewing. According to this site:
Fr Thomas More—the last descendant in the direct male line of St.Thomas More, Lord Chancellor of England—died on 20 May 1795 in Bath. He had been the Jesuit provincial superior at the time of the suppression of the Society in 1773.
Thomas More was the eldest of the five children of Thomas and Catherine (née Giffard) of Barnborough or Bamburg Hall in the West Riding of Yorkshire. Born on 19 September 1722, he was followed by Christopher, Bridget, Catherine and Mary. Both sons became Jesuits. Bridget married twice—Peter Metcalfe and Robert Dalton and had descendants; she died in 1797. Catherine died unmarried in 1786. Mary became Sister Mary Augustine of the Austin Canonesses at Bruges and died in 1807. Their home, Barnborough Hall, had been in the family since John, the only son of St. Thomas, had acquired it by his marriage to Anne Cresacre and it remained so until the nineteenth century.
In one of the appendices to a book written after More's beatification by Father Thomas Edward Bridgett, you may read about all the relics of St. Thomas More that Father Thomas More, SJ gave to Stonyhurst College, including their family history and provenance.
I really think I may have to plan a visit to Washington, DC to see this exhibit, visit the National Shrine, etc.