This goes to my favorite question about nonprofits:  Whose Organization Is It?  (See Ready Reference Page: “The Key Question: Whose Organization Is It?”)  There isn’t any absolute answer to this question. 

It isn’t clear to me whether your auxiliary is now a separate legal entity that is exempt under a group exemption or merely a part of the parent charity that is exempt as part of the charity itself.  If it is within the charity itself, it is ultimately controlled by the charity and has no individual existence.

If it has a separate legal existence, it will be more independent if it has its own exempt status and may be less subject to the influence or control of the parent entity.  If everything is fine now, separate exempt status may be unnecessary.  But if the leaders of the auxiliary want to be more independent, separate exemption will probably be helpful.  From the point of view of the parent entity, that could be either good or bad.  No one answer is necessarily better than another.  Try to find out what people on both sides really want.