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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 these overwhelming situation.
No doubt it is very unfortunate the way things have evolved in your relationship, but you are being wise and responsible when facing reality and coming to terms with the fact that it was not working but mostly wounding you, undermining your health and life, and when there is not real reciprocity around respect, honesty, affection, understanding support and commitment, there is no way a relationship could develop and grow as a healthy and fulfilling experience, and as hard as it is, children become the helpless victims in scenarios like this.
As you described here, their mother not only abandoned them, but has been using them as a way to control, manipulate and undermine your relationship with them and with their father, and unhappily he has been enabling it the whole time by being this dishonest, codependent and neglectful about the children.
You do have a unique bond with these children, it sounds like you truly care and have felt and taken care of them as your own, and the grief you are now experiencing is just very painful, as well as your concerns around their well-being.
Please, be fair, gentle, patient, understanding, compassionate and unconditionally supportive with yourself, since it is from there that you would be able to heal and cope with the unavoidable pain and challenges your situation presents, which do not depend on you, but on the children's parents. It is very sad and overwhelmingly frustrating, but the end of your relationship would not promote your relationship with them, but this is something you cannot control.
It is time for you to focus on doing your best to take good care of yourself and to keep as much contact as possible with them, as much as allowed by their father. If he has enough insight and healthy affection towards them, he would not retaliate limiting your communication as possible, but I am afraid that based on the tenor of your message, he lacks much maturity and assertiveness, which could easily literally deeply limit your relationship with them. The only way to know would be through experience itself, doing your best to keep a respectful, healthy and friendly relationship with him, in order to be able to share with them. Again, this is what you could try and promote, but it will be him who chooses what would happen with them at every level, including your relationship.
I believe you have the right and responsibility to talk to them and make sure you express to them how this is absolutely about your relationship with their father not working, and nothing about them, showing them how sad and frustrated you feel because of it, and that you hope you could continue sharing as much as possible. That you would always be there for them as much as their parents and your circumstances allow it.
The contact you would offer would depend on what their father allows, and what you were able and willing to offer based on your reality, needs ad expectations. Does it make sense?