The question you should ask yourself is what your Capricorn man wants. It sounds like you two totally disagree on a course of action, and one of you must yield to the other. Capricorns do not easily surrender, unfortunately.
Capricorn rules the mountain, and the Goat wants to be on top. He’s worked long and hard to get there, so what incentive does he have to give up his status?
Saturn rules our insecurities that we strive to overcome. The feeling that deep inside he’s not good enough — that’s the soft sticky interior underneath Capricorn’s hard surface. If he gives in to you, he needs to maintain his self-confidence in the process, or else he’ll feel less-than. Your Capricorn man will only give in if you can find a way for him to save face while he succumbs to you.
Libra’s “win win” may not appeal to Capricorn, but he does want to be seen as a benevolent leader. As much as he likes his position, he realizes that his authority only lasts as long as his organization thrives. If the relationship’s stock price increases as a result of his temporary relinquishment of power, then he may be willing to step down — just this once.