I agree with the idea of working within the dyad instead of trying to veto. It is at this point is not really working. I think a more sensible way to deal with it is to communicate your needs: time, etc. so that you can feel more secure. Ask for some solid boundaries if she wants to continue the relationship and see if she can keep them (but not necessarily a veto).
However, I also understand your standpoint. When rules have been established and these change it can be pretty upsetting. It is also about a spouse's commitment. On this forum the talk is often about (preferably) non-hierarchical arrangements, honest and fully openly-negotiated ENMs, and ideal expanding poly-structures where everyone is happy and able to sort out their differences.
However, a marriage is marriage. Many people come from a very different place. There are commitments agreed to. In a marriage sometimes hard work and sacrifices need to be made. It is not always about your needs, or your feelings. There is a bit of a gulf between expectations in a marriage and the ideal poly world. Unicorn hunting disasters, opening up roller coasters and hotwifing/swinging leading to emotions endangering the marriage are all around in forums like this. Many people set out with monogamy and then they realize their polysexual/amorous needs. But shifting is not easy, because you were building something very different.
But still a marriage is a marriage and I think some people take it a bit lightly, like okay feelings are different and then we change the structure around as needed. Or, okay a unicorn/third party is here so the marriage now becomes non-hierarchical. Often these are a bit naive assumptions. When they read about successful poly relationships they sometimes do not see the past failures, hard lessons learnt, or just the fact that the poly structure did not start out with a married couple but was built from scratch.
I'm not saying it is impossible or should never be done in marriage, but there is a certain weight on the married couple. They did give promises to each other and sometimes they simply need sacrifices to keep the promises. Long monogamous marriages always have sacrifices, given up needs etc.
So, I do think that at this point there is a need to recommit to the marriage at least in observable actions (like keeping time boundaries or no chatting in front of you etc). You can let your wife explore things or love someone else but only within reasonable commitment boundaries. If she ignores your needs, treats you as if you did not exists and throws herself more and more into her other relationship gradually neglecting more and more boundaries, changing all the rules, then she is not fulfilling her part of the marriage and then hard decisions must be taken. I think in this situation a veto is something that is also sensible. Because if all your needs are neglected and then you just accept all her boundaries but get back nothing then that is a problem. You veto and see what happens. Some people recommit, some people cannot accept.
I think you need to tell her that if she has a boyfriend, then you also expect her to want to build the marriage with you together, accept some firm boundaries (time, commitments, holidays, etc.). I know this might be unfair to the third person, but the fact is that again, the third person is not going into a non-hierarchical polyamorous relationship but he is dealing with a married couple. This is why people dislike unicorn hunting, or unicorns struggle so much, by the way. It is often hierarchical, there is a special bond between husband and wife. And it is often naive to expect that suddenly it will be like with well-seasoned polyamorous people.
Later, if things work out well then, you can move into a more non-hierarchical arrangement, or maybe have another partner on your side, but at this point I think we have to deal with the marriage issue. And do things slowly.
