Hi. Your story sounds all too familiar. I did not exercise veto power, but my husband and his girlfriend ended up breaking up in large part, due to the impact of their continued relationship on our marriage. The result is, that we are living in the same house, but communication has all but stopped. I don't know what the answer is, but when things begin with dishonesty, the foundation is unstable. If their relationship strips yours of potential, then I'd address it in a real way. In my opinion, an individual who is willing to be a part of a cheating dynamic, is not truly suited for poly.