I do not find her greedy. If anybody is greedy, it is you, because you want her all to yourself, which is a bit greedy, although, of course, completely normal and understandable, so I am not saying it by way of judging you.

It seems that the main problem lies in your spending too little time alone with her. You can express your true feelings towards her only when alone with her. His presence frustrates you, curtails your self expression, etc. Can you start spending considerable more alone time with her?

You also need friends and activities that would be completely separate from this menage a trois.

Good luck!