Keep in mind that she's not the only one with a veto. You have one as well over your own relationship with him, and whether you want to be part of it. If you don't like having the sword of Damocles hanging over you, then there is the option to move away from the situation.
It may be worth discussing what if any thought they've given to their veto arrangement, including whether they have a sunset clause, where after a certain amount of time in a given relationship, the veto is no longer a viable solution. It may not assist much with your current situation, or this partner in the short term, but it'll be a handy clarification to make should you find yourself in similar situations in the future.