We recently were in a discussion with an inspector lead (district supervisor, etc.) and asked what the procedure should be to have an inspector replaced due a conflict, etc.
She said that the best way would be to first see if the situation can not be resolved (and document the discussion) without briniging her into the mix and indicate to the conflicted inspector that you have checked with the area person to establish the basis for the discussion and what next steps would be.
This of course would put the conflicted inspector on notice that you have done your due diligence in seeing what the steps are prior to taking those steps if your documented conversation does not work out.
She indicated this as best course, because once we asked for her intervention then she needs to alert her higher up and from that I got, this is where it gets real serious real fast.
As it turned out our client was able to have a good conversation (documented) with the conflicted inspector and things appear to be better now.