Good, now we have 1st round, you still can contest the custody with all you have been saying. It is simple, they just have to have the children in a room with a two-way mirror, where they can see him but he can't see them and the judge can be in the room with the children to see how they will react when they see him. You can request that to your lawyer, to show that he isn't what he portrays and that it would be subjecting the children to pyschological damage.
Yes the joint custody does protect you in a sense to have you booted out..but if they did it would not only be mental cruelty to the children but to you too, so there is no winner here and like I said, the judges are more in favor for the childrend to stay with the mother and the fact you are in a shelter proves it..now, you have to get the lawyer to convince the judge to do this if the children are afraid of him they will react when they see him.
Or the lawyer can contest the joint custody on the grounds that the father doesn't care for the children and that it would be harmful for the children and that it should be ordered that when the children are of age to reason themselves, they will make their own decision and you can ask for a pyschologist to evaluate the children. How old are they? Now your immigration lawyer can help you with this by refering a lawyer who specailizes in children's welfare and can represent the children as their lawyer. It can be done.
Now I need to know exactly what he did for you to have left and also to the children.
It is normal to panick when you don't know the law. Not many people know it but we have good laws here to protect women and children. What you need is a lawyer who has the reputation of winning these kind of cases. And don't worry about being booted out. Your immigration lawyer should handle all of that, it is better for him as they will see you have representation and will wait the outcome.
So I am waiting for you to answer me.