There's even a dispute over which issues are in dispute. He says they made a verbal deal to divvy up the money and take care of their teenage son, but she says they never did, according to divorce proceedings quoted in U.S. court documents.
And now, she and her lawyers say Russian law entitles her to half of the couple's "marital property," including "significant assets" inside the United States.
Vladimir Potanin is estimated to be worth more than $14 billion thanks to his private investment company, Interros, and its related companies.
He built an entire ski resort in Sochi for the global games now underway, and he has long promised to give the vast majority of his money to charity.
But according to Natalia Potanina, her husband warned she can't prove anything about his wealth.
"My husband has told me that unless I voluntarily accept his oral promises regarding support, he will make sure that I receive nothing," she said in a sworn declaration filed in U.S. court. "I consider his terms grossly unfair."
The spokesperson for her husband took issue with that, saying Natalia Potanina "is now a very wealthy woman" herself and "has been well provided for."
Nevertheless, Potanina is "mak[ing] an investigation of Vladimir's assets," as she put it. And she's prepared subpoenas for two executives at the New York private equity firm Altpoint, whose funds reportedly receive substantial investment from Interros.
Altpoint's portfolio includes prominent U.S. companies owned by Potanin, including Ford Models, the agency that represented Christie Brinkley, Bar Refaeli, Paris Hilton and Lindsay Lohan earlier in their careers.
The subpoenas demand that Altpoint Chief Financial Officer Eric Chan and Managing Director Yuki Narula testify in a deposition and hand over 13 categories of documents, including any emails discussing the location of Potanin's assets and income he has made in recent years.
On Thursday, a lawyer for Potanina, speaking to Russian media, suggested Vladimir Potanin might be trying to hide his wealth through charities around the world.
But a person familiar with Potanin's charitable giving called that "ridiculous," noting his "long history of philanthropy" in Russia and the United States, beginning well before the marriage fell apart.
Last year, he joined The Giving Pledge, a global charity effort launched by Bill Gates and Warren Buffett.
A hearing on the divorce is set for Feb. 25 in Moscow.
Asked whether the two executives will comply with the subpoenas or file an objection in court, an Altpoint spokesman declined to comment.
U.S. law says "any interested person" -- even someone overseas -- can seek relevant testimony and documents from someone inside the United States for a proceeding outside the country.
Potanina is currently living in the United States, after undergoing surgery weeks ago at U.S. medical facility. It's unclear where the couple's three children -- two of them now adults -- are living.