It would seem that Roswell Lee towards the end of the war assumed responsibility for the defense of the western and northwestern frontier of the I. T. Perhaps it happened during the command reshuffle after Maxey was deposed as CIC in I.T.? Anyway, it was more likely a sub-district command, i.e. more administrative than operational. I have not seen it referred to as a brigade before, and I doubt that it deserves that designation.
Washington's Reserve Squadron was stationed in and around Fort Cobb during its entire career. Broke Arm's Osage Battalion apparently operated in the northern and nortwestern part of I. T. and probably in southern Kansas. I have found very few references to this battalion, but they apparently were a loosely organized, far ranging scouting battalion. For a while it was assigned to Watie's brigade, but there is no record of Broke Arm's Osages ever joining forces with Watie's brigade in any pitched battles. More likely, the assignment was for administrative and logistical purposes, and no doubt Watie employed them as "eyes and ears".
J. W. Cooper's battalion I have not previously heard of. Can someone enlighten me on this one?