Hi OP. I've read the whole thread, and have been thinking about you this evening. Like @whycantwegoonasthree, i'm also polyamorous (though not with as much experience). To give you some context on my life and where I'm coming from - because i think non-monogamous perspectives might be just as helpful as those reading this through a monogamous marriage lens - i have been poly for about 2.5 years. I currently have three partners - one I've been with for 2 years, and two more recent ones who I have been dating since July-ish (partner is a bit of a strong word for both of these, but....). I had another partner who I split up with earlier in the summer, who was my 'original' partner (though i was single when we got together, and he is poly).
so...a number of thoughts.
The first is that you can, certainly, 'cheat' in a poly relationship - and that is through violating or breaking boundaries. Though, falling in love isn't usually one of them, given the context of poly relationships being about multiple loving, committed relationships. These kinds of rules are more common in other forms of ethical non-monogamy (such as swinging, open relationships), where the rules are to protect the primary/original relationship. I don't personally consider them super helpful, because i think emotions are hard to control, and falling in love is something that happens to be quite easily.
For some people, breaking these rules or agreements is enough to end the relationship. For others, it's about recognising that relationships, and the terms under which we operate in them, change all the time. You have already seen this happen in your own marriage, when you realised you didn't want to have a sexual relationship anymore. For them, what then happens is a renegotiation of the relationship with the new knowledge - as you did in deciding on an open relationship.
Ok, so there's that - which is a complicated question in itself. Do you feel like there was enough deception and dishonesty to feel like the respect in the relationship is irreparably broken, or do you think you still want to try and find a way through? Coincidentally, the multiamory episode last week, the podcast @whycan'twegoonasthree mentioned, was about cheating in ENM. might be worth a listen: www.multiamory.com/podcast/341-cheating-in-non-monogamous-relationships
ok, so there's that element to this - whether or not this is 'cheating'. and you have to decide how you feel about that. but then there is the question of how you go on, if you think that this is something you don't want to end your relationship over.
Firstly, I will say that I'm really not a fan of veto powers. It doesn't mesh with how i see relationship structures, and I don't like such prescriptive hierarchies. I won't date anyone who has a relationship where my metamour (my partner's partner) can exercise a veto over our relationship. you might feel differently, but exercising a veto is a difficult thing to do without damaging the relationship - forcing someone to choose between two people they love, even if one relationship is much newer, is often the road to resentment. It's the same as an ultimatum about anything in a relationship (more children, moving country etc). it so often doesn't work
Coping with the idea that your partner is falling in love with someone else, and the insecurity that can bring, is hard. and it might change your relationship with your husband; your pattern of seeing each other may change. trusting him not to leave you though...you have to trust him. just as everyone, really, has to trust the person they love. marriage doesn't really tie us to people in the way we think. the relationship format doesn't really give us the security we think it does. divorces happen. marriages end.
My partner once said to me that he 'felt secure in our relationship because even though I could choose to be with anyone, and often did, i also kept choosing him, over and over again'. I don't choose him to be the only one, but we both accept that it is possible to fall in love with other people, and still be in love with each other.
That is perhaps a hard thing to understand, especially if you've been in a largely monogamous marriage, and one which is, up until recently, emotionally monogamous, even if not sexually so. and it might not be something you can ever accept or feel happy with. but, given that you want to stay with your husband, and it's not impossible that your DADT arrangement may bleed into emotions again at some point, it's probably worth thinking carefully about what it is that makes you feel insecure.
The reason i say this, is because we have an understanding in monogamous culture that if you partner is in love with someone else, it must be because they don't really love you anymore. So is your insecurity being triggered because you are worried that he can't be telling the truth - that if he's falling in love with her, he must be preparing to leave you/will leave you eventually? It might be that this is how your husband's mind works, but it might not be. he might genuinely be able to love both of you.
Ok. Final point. If he does love her, it is possible that your relationship - and his relationship with her - will change. As we started with, relationships change all the time. This is actually a key essence of polyamory; that relationships change, as do our feelings. someone who we used to live with full time, may be someone in 10 years time that we have a close, affectionate, loving friendship with, but we only live with half the year, so we can see another partner. What is generally accepted, though, is that these discussions happen openly. In operating a 'don't ask, don't tell' policy, it's been hard for you and your husband to have these discussions - and he has, in the process, drifted from your original agreement probably assuming he could keep the feelings in check. As others have said, if you decide you do want to try and continue together, you will have to learn to be much more open - and that your relationship is going through a (or rather its second) fundamental change.
ok...that was long, and maybe not as coherent as i hoped, but i have to go have a bath, so apologies!