the entire problem for the native americans is that their way of life doesn't mesh with the European lifestyle, and the Europeans advanced enough to have the manpower and the gunpower to do away with them. As long as there's conflict, which is a basic result of difference of lifestyle/power, the NA are going to end up on the shitty end of the stick. So, if the US never hears of Andrew Jackson, the NA are still going to be abused. Not as badly as in the world of AJ, but eventually it's going to work out the same. we didn't have to be such dickheads to them, but as long as they practice their heritage/way of life, they are doomed to the ultimate fate.
The best bet for them is for them to assimilate, but that means loss of heritage, and they cease being native americans. Pretty much every culture that came to this country eventually lost its culture. I might say I'm a German-American, but outside of enjoying a good Bock beer, I'm no more german than my cat. Even assimilation is going to be tough, because americans were a pretty racist bunch. we were founded on the notion of all men created equal, as long as you're the right men.
So, you have two choices: assimilate, or allow them to have their own nation states, which means giving up choice pieces of land (which is why they were moved out of the Southeast, and pretty much anywhere we displaced them from). edit: OTL, we did give them all nation states, but OTL version of it was to give them the crappiest piece of land possible. that's disaster for their heritage, because they can't practice the same way of life on a postage stamp sized piece of useless land. and it's disaster for when they finally do decide to assimilate while staying on the reservation, because the land isn't good enough to accomplish economic viability. and then we get mad when they figure out how to use us with casinos.