B is typical micro-management kind of guy, nobody can stand it.

How's your relationship with your VP? Any chance to talk to her and clarify your own preference (if there is still a room for you to struggle)? And how high is the chance she will listen to you? Of course as a vp she has to balance different groups, but how about persuade her to recommend someone else to work under B? If B emphasize there some work can only be done by you, you tell VP it's time to train someone else too to avoid single point of failure as well as internal resourse contention/competition. Anyway, don't go back to work for B, not even shared with A.

Sorry for the English, not convenient to type Chinese now. Just my 2 cents, hope this helps.