Depending who you believe, Alice Walton is either a harpie descending on the American art world – "a hovering culture vulture", in the words of one writer for the Wall Street Journal, "poised to swoop down and seize tasty masterpieces from weak hands". Or she is a philanthropist in the grand American tradition, using her billions to build a formidable collection for the enjoyment of the general public.

Either way, she is stirring up a hornet's nest of passion, ill feeling and latent art-world snobbery as she acquires one revered masterpiece after another in preparation for the world-class art museum she plans to open some time in 2010.

It would be one thing if Walton was the scion of an established East Coast family, a robber baron in the grand tradition of American capitalism who had at least had the good taste to settle in a bastion of recognisable civilisation such as New York, or Washington, or San Francisco.

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But she is not. Walton is the daughter of the late Sam Walton, the founder of Wal-Mart, and she plans to put her Crystal Bridges Museum of American Art slap bang in the middle of Bentonville, the tiny town in northwestern Arkansas where her daddy first made his mark selling discount groceries and later established the world headquarters of what is now the world's largest retailer.

Wal-Mart is not only huge – if it was a country, it would have the 19th largest economy in the world – it is also a byword for everything that the American cultural elite tends to detest, a soulless monument to the banality of modern life with its big-box suburban supercentres, its low-grade, low-price products, its tendency to chase small family-owned concerns out of business and its reliance on cheap labour that often has to turn to government-sponsored relief programmes like food stamps to keep body and soul together.

The fact remains, though, that Alice Walton is the second richest woman in the world (second only to her mother), with a personal fortune of more than $15bn (£7.5bn) that gives her a licence to buy more or less whatever she pleases.

The art world has been eyeing her suspiciously ever since she snapped up an iconic 19th century painting – Asher B Durand's Kindred Spirits – from the New York Public Library in 2005, paying $35m in cash to blow away rival bids from the Metropolitan Museum of Art and Washington's National Gallery, which had hoped to keep the painting in a public collection.

Last year, it was Philadelphia's turn to be outraged as she tried – and narrowly failed – to acquire another iconic piece, Thomas Eakins' The Gross Clinic, regarded by some critics as the best American painting of the 19th century with its depiction of a Philadelphia surgeon, Thomas Gross, giving a blood-soaked surgical demonstration to his students. Walton offered $68m to Philadelphia's Thomas Jefferson University for that picture, four or five times more than had ever been paid for an American painting of the same period, and lost out only after the Philadelphia Museum of Art and the Pennsylvania Academy of the Fine Arts – spurred by a public outcry – banded together to match her price. She ended up with a lesser Eakins as a consolation prize.

Now Walton is embroiled in a dogfight with the GeorgiaO'Keeffe Museum in Santa Fe, New Mexico, over the fate of a collection bequeathed by O'Keeffe to Fisk University in Nashville, an institution founded to educate the children of black slaves which has now fallen on financial hard times. Fisk has agreed, in principle, to sell Walton a half-share in the 101-piece collection, which includes works by Picasso, Cézanne, Renoir and Toulouse-Lautrec as well as O'Keeffe's own 1927 masterpiece Radiator Building – Night, New York. Walton has agreed to pay a cool $30m.

The Georgia O'Keeffe Museum, however, argues that under the terms of the bequest Fisk has no right to sell anything – except to the Georgia O'Keeffe Museum, which believes it enjoys special status as a "successor in interest" to the foundationO'Keeffe set up to manage her estate following her death in 1986. It is suing to try to block the deal. The case isn't set to reach court until February next year, but the bad blood generated by the dispute is already remarkable.

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The Santa Fe museum's director, Saul Cohen, has openly accused Walton of interfering in a tentative deal he had in place with Fisk, whereby the Radiator Building painting would have moved to the museum in New Mexico and Fisk would be given permission to sell off one other picture, by the modernist Marsden Hartley, on the open market. Lawyers for both Fisk and Ms Walton have shot back that the collection established by O'Keeffe (and before that by her collector husband, Alfred Stieglitz) would remain intact and fully accessible to the public. In a court filing they derided the museum, saying it was "not a credible arbiter of O'Keeffe's intent".

What many of Walton's critics bemoan is, in the end, the vulgarity of money. Walton is far from the first rich American to buy herself a first-class art collection – J P Morgan, the Rockefellers, even the Las Vegas casino mogul Steve Wynn have preceded her – nor even the first to take works of art out of their most obvious setting and plonk them down in a museum. (The recent efforts by Italy and Greece to recover stolen treasures from the Getty museums in Los Angeles attest to that.)

Walton's initiative is, in the end, no worse than art-buying sprees of the past and may be considerably better because she plans to put everything on public display. She is spending well over $50m to build her museum, a complex of six glass and wood pavilions set in the wooded hills that reach all the way into the centre of Bentonville. The place, being designed by the Boston-based architect Moshe Safdie, promises to be a considerable tourist draw – Walton says she expects a quarter of a million visitors a year to admire a collection that already features works by Winslow Homer, Edward Hopper and George Bellows alongside her extensive collection of Native American art.

The greatest unspoken objection is, of course, that no self-respecting East Coast art snob would be seen dead in rural Arkansas. The fact that Bentonville is three hours' drive from Kansas City, and the same distance from Memphis, won't come as much consolation to the collectors of Manhattan's Upper East Side. There are also questions about the pedigree of the woman herself.

Alice Walton is an intensely private person, so it is almost impossible to judge her with any accuracy. She doesn't work in any recognisable, conventional way – she's lived for the past decade on a horse farm in Texas, where she raises champion "cutters" – horses trained to corral cattle. She's been married and divorced at least twice.

She's had more than a few problems with drink and fast cars, including one episode when she struck and killed a 50-year-old mother of two with her Porsche (no charges were ever brought) and another when she was pulled over for drink-driving in 1998 after hitting a gas meter and tried to lord it over her arresting officer with the immortal words: "I'm Alice Walton, bitch!" When she was prosecuted, she ended up having to pay a glaringly modest $925 fine. Ms Walton moved to Texas and settled on her ranch.

The art museum is, in many ways, her way of making peace with her home town and an attempt at personal redemption. "Bentonville and this region of the state is my home, always has been, always will be," she said at a rare public appearance to announce her museum project in 2005. The Arkansas authorities have done their bit to make her welcome. Shortly after she acquired Kindred Spirits, they changed state law so she would have to pay no tax on the Durand or any art work she brought into the state.

It's not often that a genuine masterpiece comes on the market, but with the prices Walton is offering she is likely to induce several institutions, notably cash-strapped universities, to consider a sale or two – a practice that is generally frowned upon.

Now she has her eye on four paintings being auctioned off by Randolph College in Lynchburg, Virginia, over the objections of the school's art curators, many of whom have resigned in protest. Walton visited the campus last May and told the college authorities then she wouldn't consider parting with her money unless she could get hold of some of their prestigious American collection outright. That opportunity is now opening up to her.