Out of curiosity
Is she toxic to him or bad for him? Ideally not looking at this through your eyes? Just wondering because in the end it is their relationship. You might not like parts of it, but you don't really have control. You could obviously point out why she is toxic and why she is wrong or bad, but in the end anything that happens needs to be his decision. Otherwise you end up with a slew of other problems.
Also, instead of thinking of it as vetoing, maybe you need to create some separation. If you two don't get along, it would be polite if he didn't invite her out to the same spots at the same time as you. It would only be polite.
As to public venues. I have friends that don't like each other, I have in the past asked one group to please not come out as it always causes tension with the other group. Personally as the hinge between those groups, that causes a lot of stress for me. (no none are romantic)
Sometimes the hinges forget this responsibility. Especially in a split V where the legs really don't like each other. If the hinge wants to maintain a relationship where sides dislike each other than its the hinges job to keep the peace. You cant force people who dislike each other to actually be friends. Thats just a fools game.
Hopefully Breathes can respect that enough to work with you so you can remain separated from her.