The American Indian Policy of the early 1800's was similar to most other European powers of the time. That's to say that there was forced or nearly forced assimilation of religion, agriculture and laws. Native Peoples were expected to adopt the language and customs of the more powerful colonizer in a very short time frame, often within a lifetime of running into the foreign power.
This is different than in the Ancient world where for example, the expanding Roman Empire would often let native religion and customs flourish, assimilating the natives over several lifetimes. This assimilation was often carried out through incentives such as positions of influence that were rewarded or simply leading by example and making the natives wish to adopt customs of 'civilization' rather than doling out punishments. The military would often resettle lands that were conquered and over 100 yrs or so, the conquered lands began to look more roman and less 'barbarian'.
I think to look at the possibilities for the way things could have turned out differently in America greatly depended on the individual Indian Nation/Tribe.
I'm of the belief that tribes like the Apaches in the Southwest never could have lived peacefully amongst settlers. This is because their way of life was nomadic and there wasn't really a concept of land ownership or boundaries like there is in Western Culture. Raiding rival tribes was an accepted part of life. There's no possible way that the American people, who came West precisely to own and homestead land could ever have lived in peace with them.
In fact, if you want to look at an ancient parallel, you could look to the Germans in the Roman Empire who even when defeated, Rome could never truly colonize and assimilate until very late in its history. This is because their entire way of life depended on warfare. Agriculture and settlement were actually forbidden by the chieftains because they were afraid that it would make their people too peaceable and unprepared for war.
I do however believe that relations between the '5 civilized tribes' could have gone very differently than they did. The Cherokee, Chicksaw, Choktaw, Seminole and Creek tribes had all adopted regular, settled agriculture to varying degrees. These are the nations that the Supreme Court and many leading citizens of Jackson's time wanted to maintain treaties and trade with.
In my opinion, if it weren't for such a pro Indian removal Executive in the White House at this time that marshaled the US Army for his purposes, these tribes could have remained in the Southeast through the Civil War and possibly to this day. I would also say that if it weren't for the British and Spanish manipulating and convincing the Seminoles and Creeks to fight the United States in the War of 1812, sympathy for Jackson's policies would most likely have been less.
These tribes had villages and cities, some had adopted the Christian religion to varying degrees, many had adopted the Western form of dress and many had learned English, conversed regularly and traded with the White settlers that lived near them.
It's very easy to imagine if not for the forced resettlement, these tribes holding on to much of their culture and evolving and modernizing along with the White Settlers. It's interesting to think about what the country would look like now if the Southeast were some sort of semi autonomous or fully autonomous country.
I think that most of the Tribes would simply have been eventually annexed by the United States and would be sort of like Puerto Rico or Hawaii today- places with their own history and identity, but also are undeniably American.
It's a shame that the populists and speculators won the day in Jackson's time and the stage was set for ethnic cleansing and the forced removal of people from their land.