Two step audience is bad for details/outcome of the audience but good for managing whom you wish to grant the audience. It would work best if most audiences were just bonuses (like: grant audience to a governor and the morale on planet X improves by +2 and overall empire corruption falls by -1) or an instant decision (the survey ship encountered a planet with an ancient relic machinery, by granting the audience you tell them to investigate it further - also granting the audience locks 5 scout ships for X turns).
It sounds reasonable. It would depend on the presentation though. You'd have to present enough information in the "audience requesting" phase for playings to make an informed decision. It can't just say, "General Grahm is requesting an audience", or you won't know what makes Grahm's audience of more worth to you than Grand Minister Sam's audience request. It has to say, "General Grahm is requesting more resources for the war effort in the Alpha Centauri system."
Then, in the "audience granting" phase, it'd have to remind you (using the exact same text snippet) why you granted the audience.
[General Grahm is requesting more resources for the war effort in the Alpha Centauri system.] [Grant Audience]
[Another person you already agreed to give an audience to] [Grant Audience]
[The third person you agreed to give an audience to] [Grant Audience]
As for granting audience to get a report... well, I think (or rather, I'm quite sure) it should not use any focus points and therefore would not need any button at all (just "more details" button). Generally, I hesitate if I should put reports in audience mechanic in the first place... Maybe it should be done some other way?
That makes sense. Maybe you can show all the reports first, before accepting audiences, breaking it into two distinct phases.