If you need it now to do your job, one strategy companies use is to escalate the request to the common point of reporting (even if it is the CEO). You and the person you are in conflict with (the other manager) need to write an escalation doc describing the conflict. It won't get to the CEO as there will be increasing levels of embarrassment up the report chain. If it does hit the point of common reporting and she says end of Q1 2022 you've got to accept her decision