I'm on a project where my role includes managing a cooperation with another company. I'm the sole person responsible for that.
Now something strange happened. The company "decided", without consultation, not to scale down their delivery, which I formally requested from them - which was consulted with my boss and other leaders and expressed according to the process we've always been following. They claimed that another team member "told them" they shouldn't scale down (the colleague denies that). I caught that before chaos occurred (overproduction and conflict). However, since that time they have been raising the topic of "we don't know if User is really accountable" and criticising me for "sending contradictory messages" during every meeting.
I asked my boss if they could clarify who in our team is responsible for communicating decisions concerning the cooperation, to both us and the other company, to avoid misunderstanding and conflict.
My boss is very reluctant to do that. They do confirm to me that I'm responsible, but not to the other organization, even when I directly asked them if they could do that. When during meetings I clarified the other company that they should take my decisions as our official decisions, my boss visibly held back, never confirmed it publicly - instead he criticized my stressing that. I feel that's making my job difficult since the other company questions my every decision.
How can I fix it?