Hello, I am Rafael. Thanks for asking your question - I'm here to support you. (Information posted here is not private or confidential but public).
I am very sorry to know about this sad and frustrating situation.
Could you please tell me for how long have you been together and how long ago did these serious issues start?
Based on your story, it seems you are very clear that you have only stayed in this relationship because of your child, and this shows how unhappy and hopeless you feel about it.
You have tried to work with her on your issues, even to get counselling but she refuses and actually feels she does not need to change nor any support around your relationship.
This is why I do not see how your relationship could heal and significantly improve in the present, and even less in the long run, even more because while on one hand you are willing to do your best to keep going regardless your issues because of caring about your child and setting him/her as your top priority, she does not feel the same way, and continues to push you even more with her lack of understanding, respect, and jealousy.
Being this your reality, knowing that regardless your intentions and efforts she seems unable and unwilling to even recognize her own issues and mistakes int he relationship, so to take responsibility for her role in it, from her feelings and choices, to her actions and real neglect towards you and your relationship, I do not see how this situation could work for your child either. It's not been working for you, and it would be unrealistic to think it would be fine with time while she remains the same. It would get worse and not better unless she makes dramatic changes, and it seems that it would not happen without professional support, one she refuses to even consider.
Many times many people stay in relationships and marriages exclusively because of their children, truly believing that by doing so they are protecting and ensuring their children would be fine, loved and grow healthy and happy rather than traumatized by separation. Unhappily in reality many times things do not work that way at all, since children's development, grow and happiness do not only depend on having their parents' physical presence and direct support under the same roof, but mostly on how well each parent feels and lives at the individual level, how they interact and share with each other as partners, and the very modeling they offer through every one of their behaviors, which literally shape a child's mind, heart and personality. This is why I use to say that a person cannot be a truly good parent without being a healthy and fulfilled person first, and a good partner/spouse or healthy friend of the other parent too.
This is why I believe you need to carefully assess your core needs and priorities in this situation, being realistic, assertive and very proactive too. If necessary please consider some individual counselling of psychotherapy for you to work on yourself and through this process. One you do this, you would talk to her being fully honest and open, setting clear boundaries and limits, explaining to her what you need, want, and are willing to do to support her and your child, hoping she could do the same, for both of you to work together on healing the relationship, so for your child and family to be fine, healthy and truly happy.
If she is able and willing to listen, to take you seriously, show respect, understanding and hold accountability for her role in the relationship, feeling enough affection and caring towards you and your child, then she would agree to work on her personal issues with you as a team, for your own and your child's well-being, without rejecting any necessary help she may require in this process. But if she remains the same, or her actions do not consistent follow her words abut committing to make necessary changes, then you would need to focus on taking better care of yourself, and doing necessary changes to continue to take good care of your child, without enabling-staying in the relationship.
Does it make sense?
we have been together 12 years