Question

if the tribal government don't recognize judicial board does separation of powers still work

Answer 1

I don't think we can answer this question. What constitutes the "tribal government"? An executive council or chief? Is it a legislative body? Is the judicial board not part of the tribal government? If the "government" refuses to recognize part of itself, the judicial board, and assumes those powers unto itself, then the separation of powers has broken down. But, not knowing how this "tribal government" is constituted and what powers it has, and the role of the "judicial board", it's impossible to know the answer you seek.