The United States should decide... either as a constitutional amendment or as a popular vote. If the tribes have input, that should be taken into account. But it's not like Native Americans have any more right to exist than any other person born in the United States.
In general, states can enforce their borders, but it's safe to say that the Native Americans failed at that considerably, and those wars have concluded and the USA has firmly won. This is not a value judgement, or a statement of what should have happened. It is simply observation.
Ultimately, the tribal system is a compromise to make things work as they are now. But, in the long term, this is never going to work out. Like I said, there is nothing good to come of this. At some point, some generation will have to bite the bullet and allow separation or pressure integration. This system we've created which encourages pseudo separation and shies away from integration really can't work out in the long run. It will lead to factionalism, in-fighting and eventually war or genocide.
A better solution would be to put in place incentives for Indians to leave the reservations and integrate with American society, with the eventual goal to privatize native lands or to make them public like any other land. Again... the system we have now, to hold land into perpetuity will not work.
Ultimately, tribal belonging is currently tied to how 'pure' one's blood is. This is the last vestige of racial preference in this country. These sorts of things invariably lead to bad outcomes in the long run.
Is it sad that cultures die? Yeah, perhaps, but cultures have always died. Thus is the way of the world. As each one dies, more will be formed. Oh well, times change.