Ms. Mugrabi, 39, who has two children, 9 and 11, with her estranged husband, wants her share. There is no prenuptial agreement. But before she can ask for a number in the divorce settlement, her lawyers say they need to evaluate her husband’s net worth, which involves exposing the Mugrabi family’s sophisticated structure of asset ownership by offshore corporations. Such revelations would offer a rare window into how art-world titans like the Mugrabis shield their finances from public scrutiny. She became accustomed to luxury at an early age, having grown up the daughter of a prosperous plastic surgeon named Charles Scher. The couple wed in 2005. Ms. Mugrabi says she noticed her husband’s more flamboyant brother, Alberto, first, but it was David who got her number. She had just turned 22 and had recently graduated from the New York Restaurant School. The Mugrabis’ art-world ascent began with David’s father, Jose, who emigrated to Colombia from Jerusalem in 1955 and made a fortune in textiles. After moving to the United States in the 1980s, Jose shifted his attention to the art market. The family has become so influential in setting global prices that The Times of London once described them as controlling “the art world equivalent of the Dow.” In divorce preceedings Ms. Mugrabi has been accompanied by her mother, Jane Scher; her sister, Mia Rowe; and about six lawyers.