She is not causing you your jealousy and insecurity - feeling insecure and jealous is on you. The only way to feel more secure and less jealous is to look inward and work on you.
Likewise, her feeling stifled and like she cannot be herself is on her. It may be that she wants other relationships in order to become more like the person she feels she is, but it also could be other outlets that could do the same thing. Essentially, she agreed to monogamy and then cheated on you rather than communicating about what she was unhappy with first.
This is not to say that you don't have issues to work on together. It seems very clear that you both do. There is a lot of blaming going on by both of you, and you are now terrified of losing everything, while she is frustrated and feels like she has been denied something she needs.
I suggest couples counseling with a therapist who is familiar with alternative lifestyles and/or polyamory, so that there is a good understanding of what you both are dealing with. Your partner should know that you can't just change the dynamic of your relationship suddenly just because she demands it. There needs to be discussion, total honesty, acknowledgement (on her part), and forgiveness (on yours) for her betrayal before either of you should consider opening up your relationship. Know that it could take a very lo-o-ong time to get there.
Most couples come to a point where they realize that certain things that have been unspoken for a long time now need to be said and looked at. It does not necessarily mean the end is near.
You might find eventually that you can cope with the drastic change in your dynamic that her having another relationship would be, but that could only come after some good hard looks at the relationship you have with her currently - but she absolutely should not be seeking another one if she is simply neglecting you. Saying that she is not sexual or intimate with you because you won't allow her to be with others seems cruel and like bullshit to me. It is more likely that she wants more out of what she has with you AND wants to be with other people, too. It isn't fair to blame you - but each person in a relationship is 100% responsible for their part in how it evolves. Have you romanced her regularly since she became a mom, dated her, told her how much she means to you, helped with housework and the children so she doesn't feel like a bedraggled housewife instead of a desirable sexual partner to you?
Furthermore, the person who is in the "hinge" position of a poly "Vee" arrangement (meaning someone who has two relationships while their two partners are not involved with each other nor anyone else) means that they now have double responsibility to manage both relationships well, and make sure both partners feel respected, loved, appreciated, valued, and given the time and attention they need to thrive in that relationship. So,if she thinks she is going to get anywhere in being able to have two relationships, she needs to give you all those things. The relationship between you needs to be loving, stable, secure, and attentive - to both of you. If your relationship is anything less than happy, strong, stable, and secure, polyamory could help bring it to its demise. People should never look to have multiple relationships out of unhappiness - that is cruel to everyone they are with.
