Dealing with difficult leadership

Dealing with an unfortunate situation where the majority of the leadership team, other than my direct chain of command, outright refuses to collaborate with other departments (namely mine) and do not believe that necessary requests for support, such as budget or program provision numbers, are reasonable requests to have, and that they have no obligation to support these requests. Our ED is conflict avoidant and would do very little to help if the issue was to be brought up to her (and it likely has by my own leadership). As a middle manager/director, I have to make requests of these people fairly regularly but have almost never received a positive response from the leadership team from other departments. This mentality has also trickled down so that ICs in other departments also refuse requests for support.