I'm wondering how well he's doing at communicating his own wants to her. She expressed her desire to him to have him all to herself. He expressed to you his belief that this would be unfair. Has he expressed it to her?
I don't blame you for wanting to tread lightly. Making enemies out of her won't help anything, and if she's already jealous and taking the alpha female tactic, she may already be gearing up for a fight. That can only end poorly.
I don't think it's unreasonable for you to request a night out with him, and for him to simply tell her that it's going to happen. It's his life, he can choose how he spends his evenings, he doesn't need her permission. If she's grown-up enough to make the trip, then she can handle herself for one night.
It's also worth noting that although she's expressed this as a desire, that's not the same as expressing it as an expectation. Most people understand that there are all kinds of things we want and they can't always happen. If she can't handle not seeing him for one night, then she's got bigger personality issues than her selfishness.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker