(Yes, Cherokee, it IS Lakota)
I've always heard it translated by the Lakota people I know as "all my relations", no other way. And it is used in prayer to indicate the inclusion of all four-leggeds, wingeds, finned, etc. in the prayer, as well as their ancestors (I believe).
I am not Lakota, though I've been around them from time to time over the years, and it was first translated to me in the early 80's, before it started being widely abused by newagers.
In my opinion, it was NEVER intended as a "brotherhood of man" sort of thing AT ALL!! "All my relations" means just that, the relations of the person making the prayer, which are the beings that that person wishes to acknowledge and considers himself to be related to.
Seems to me it's safe to say that a Lakota will consider the buffalo as his relations, but highly doubtful that he will ever so consider the wasichus.
Best to find a Lakota to speak on this, of course. I just wanted to throw my 2 cents in.