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In the first place, this is a difficult situation esp when you are functionally reporting to a boss and administratively to the other. The solution is simple but requires expert handling. Your decisions should always be in line with corporate policies and procedures, irrespective of the fact which boss is saying what.
In the short term I would say get everything in writing, by e-mail is fine. Because there is a danger of being blamed for the failure of this system. If someone asks for something tell them to e-mail you, so you have a copy.
In the longer term you will need to ask to be given one boss to report to. Everyone else can go through that boss to speak to you. I don't see how the system you describe can ever be made to work. Sorry.
Also, keep a good resume/c.v. you may need it.