Trail of Tears Goes North

This is a topic I've been thinking of off and on for several years; could the American government have shifted the majority of its Native Americans North into British territory during the 19th century?
It would have simplified things for them in the long run. Instead of shifting the Natives to smaller and smaller pieces of undesirable land every few years, round most of them up all at once and send them North. Not into present day Ontario or Quebec of course, but Ruperts Land where no one important lived.
For the Americans it would have been a nice way to solve an annoying problem. It would tweak the noses of the British without annoying them enough to do anything rash. It probably wouldn't involve much more fighting than they had to deal with IOTL. With a promise of food, tools, some money, and to never having to look at an American again, a lot of Natives might actually go peacefully, if unhappily. Not all of course, but some.
How would Britain react? Would they force the US to stop? Would they make the new inhabitants a possible force to stop any US attempt to move North? Or would they see it as a waste of money, and ignore the problem until it became too big to ignore?

Thanks in advance.

IOTL the British accepted many Lakota refugees such as Sitting Bull. But there already were Lakota in Canada. It seems likely the tribes'd have to negotiate with the British and some groups like the Cherokee'd be reluctant to go, having fought a very destructive war with them a few generations before the Trail of Tears.

Recall the debate over forced relocation took some time, actually spreading out over two presidents' administrations. It's not something the US could carry out without the British having plenty of time to respond to.

I knew the British accepted a few Natives into the country, thats what made me think of this.
I didn't know that it took THAT long to make the decision though. So no fait accompli, the British would be able to put a stop to it in time then.
Thanks.

AmIndHistoryAuthor said:

IOTL the British accepted many Lakota refugees such as Sitting Bull. But there already were Lakota in Canada. It seems likely the tribes'd have to negotiate with the British and some groups like the Cherokee'd be reluctant to go, having fought a very destructive war with them a few generations before the Trail of Tears.

Recall the debate over forced relocation took some time, actually spreading out over two presidents' administrations. It's not something the US could carry out without the British having plenty of time to respond to.

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??? There were Lakota in Canada? Where?

There are Nakota in Manitoba/southeast Saskatchewan, but I don't know of any Lakota that didn't come up from the States as refugees.