A criminal history is not relevant to family law matters unless the child was somehow involved in the crime, such as witnessing it or being a victim of it. You can't simply present a criminal history of the other party and say, "See? Look at what a terrible person she is!" It has to be evidence that is directly relevant to the current case, and while I understand that you feel those crimes are an adequate demonstration of her capacity to parent, unfortunately, the court doesn't agree.
The other thing I want to add is that character assassinations in family court are interpreted as a inability to support and encourage the child's relationship with the other parent, which is crucially, crucially important when considering the best interests of the child. Best interests are not just physical safety and the like, it's also emotional well-being, security in exercising their rights, and having their needs recognised and respected by the parents. If you're seen to denigrate and undermine the other party in such a fashion that the court suspects the child is at times subject to that conduct, then it will ordinarily order that excessive exposure to that parent is not in the child's best interests.
I don't say this to kill your hopes of attaining residency, but more to share with you what the court wants to hear. Rather than focusing on the terrible deeds of the mother, focus on how the child has been affected by it and how you hope to remedy it in the best way possible. Make sure you recognise that even if you don't like the other parent, the child definitely does, and there is benefit to the child in having a relationship with the mother, even if that benefit is just to learn what not to do in life.
This tends to be something self-represented litigants are left out of the loop on because it's something you only learn from experience in the court. If you want to get a taste of some of that experience and see how the court manages parents that are unsupportive of the child's relationship with the other parent, I would be happy to provide some family law cases for you to read over.
I hope this helps clarify the situation, at least in regards to the criminal history, and maybe helps you gain a better understanding of the court so that you can shape your case in a positive fashion.
