From a distance the teardrop-shaped peninsula looks just like any other bit of the famed Hamptons shoreline. Thick woods crowd down to the water's edge, and through the trees houses and roads can be glimpsed.

But this land is not part of the Hamptons, neither is it really part of the United States any more. This patch – in the middle of the playground to Manhattan's social elite – is proudly and fiercely Native American country.

Almost four centuries since their first contact with the white man and after a 32-year court battle that has just ended in victory, the tiny Shinnecock tribe has now been formally recognised by America's federal government.

The decision means that the Shinnecock, numbering some 1,300 members, many of whom live in deep poverty compared with their wealthy neighbours, can apply for federal funding to build schools, health centres and set up their own police force. It means their tiny 750-acre reservation is now a semi-sovereign nation within the US, just like much bigger and more famous reservations in the west.

In order to qualify the Shinnecock literally had to prove that they existed, submitting thousands of pages of tribal records. It was a process that has left a bitter legacy. "Why do we need federal recognition to show we are who we are?" said Shinnecock leader Lance Gumbs as he sat in his office in the community centre. "It's a humiliating, degrading and insensitive process. Why do Indian people have to go through that? No other peoples are treated like that."

Many believe that the lengthy and painful process that the Shinnecock have been forced to go through is explained by the tribe's position bang in the middle of the Hamptons, the string of Long Island towns where rich New Yorkers come to party away the summers. The difference between Shinnecock land and the rest of the Hamptons is jarring. The reservation, signalled by a line of stalls selling cheap cigarettes, sits side by side with the town of Southampton, heart of the Hamptons scene.

On the reservation, some roads are dusty and unpaved. The houses can be ramshackle. Unemployment can be a problem for many Shinnecock members. Outside it on the streets of Southampton, stretch limos and black Lexus prowl down streets lined with shops selling Ralph Lauren and Diane von Furstenberg. A real estate agent on Southampton's main street happily advertises a local house going for $12.2m.

Historically – and indeed pretty much since Europeans first arrived in the area in the 1600s – the Shinnecock have been on the retreat. They lost land steadily as more and more Europeans began to farm their traditional territory, eventually leading to an agreement in 1703 that saw them confined to a broad swath of land around Southampton under a 1,000-year lease. However, in 1859 the pressure of development saw that deal scrapped by the settlers and the Shinnecock reduced to their current tiny holding. For years tribal members then eked out a living working on white farms or helping local fishermen and whalers.

Now that is all set to change as a key part of federal recognition allows the Shinnecock to do the one thing that has changed Native American fortunes more than anything else in the last 100 years: build a casino. Gumbs now sees real power finally in Shinnecock hands. "We are going after everything we are entitled to," he said. "I am not a big fan of Southampton. They were happy as long as we were the good little Indians in the corner. Well, that's changed now."

It is unlikely that the Shinnecock will build their casino in the Hamptons itself, which is already notoriously crowded and traffic-clogged. Instead the simple threat of it is likely to eventually see them negotiate the right to build a casino elsewhere in Long Island, an area that is seen as ripe for the development of a gambling mecca.

Either way, it seems Shinnecock fortunes are set to be dramatically reversed. For many tribal members it is a chance to rescue what remains of the tribe's culture. Sitting in the tribal museum and cultural centre, Winonah Warren, 71, remembers being taken as a young girl to see a Shinnecock medicine man. She sees the deer that she spots in her garden as a spiritual sign.

She practises a Native American religion in which she takes peyote. It is about as far from the Hamptons scene as it is possible to get. "I love being on the reservation. Even when I am not here, I feel that my heart is," she said, touching her chest.

Some even feel that federal recognition – and the prospect of a casino – might be the beginning of a wider Shinnecock resurgence. In the white land grab of 1859 an area of land called the Shinnecock Hills was taken. Many Shinnecock held it to be sacred ground. It is now full of rich houses and the famous Shinnecock Hills golf club, with total real estate worth more than a billion dollars. The Shinnecock have sued to get it back.

For many of the Hamptons residents the prospect no doubt seems ridiculous: a relic of ancient history and long-forgotten wrongs. But not so for some of the Shinnecock. Elizabeth Haile, a 79-year-old tribal member, remembers her grandmother telling her how the Shinnecock Hills had been stolen.

Does she think the tribe will ever get them back? "Yeah," she said with no hesitation, and then added with a smile: "It is a prediction. Some people never thought we would get federally recognised."