I am prepared to believe what you say, without raising the doubts Lawmoe and others may feel it necessary to raise.
I have read of other cases like yours, in the US at least, so that helps persuade me too.
When my friend Lawmoe (- I think I can call him that now after a reasonably long period in which we have shared opinions, or engaged in arguments) - when he says this:- "The court bases custody determinations on what is in the best interests of the child." - he is using their ultimate weapon against you.
I am excluded from my daughter's life for ten years because I couldn't convince court officials seeing me was in my daughter's interests at all. That is the tremendous power encapsulated in that one sentence.
How is the rest of society to criticise a court that can claim to have "acted in the best interests of your children"?
You will find it a very large monkey to get off your back, although like Lawmoe, I do wish you luck.
The strong tend to take advantage of the weak, or those who appear weakest in this world. Maybe your ex. husband had friends in high places who could help him influence the court to grant him custody, maybe he is just more convincing than you are (my ex. was more convincing than I was I know, even though she was caught out lying to the court officials, they still sided with her).
Lawmoe is well versed in the law I believe, so will offer you fairly good advice as to your choices, or course of action. However, unlike him, I don't have much faith in the prospects for justice for people like yourself (though I hope for it).
All the best, Graham