You know Ambassadors are appointed, not elected, right? You just need the Tribal Council or Sanmatar to recall him.
That said, I don’t think Yun’s advocacy has been at all ineffectual. You say he failed to sway the Assembly. The Gallente say the allegations must be investigated. The Caldari say they will be investigating, from their side.
How, exactly, is both of the other empires saying there must be investigation a failure to convince them? They were never going to simply accept the evidence presented without conducting their own investigations. That’s not how international diplomacy works. Nobody trusts anyone else, so of course they’d need to verify it all themselves.
This is like insisting that Dark Shines is an ineffective leader because the Black Hand is conducting their own investigation into a matter.