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I will try to best answer your question.
The standard to be applied is the best interest of the child standard not the best interest of the mother stanard. It sounds like this 4 year old brother maybe a victim of sexual abuse. I think you will have an excellent chance of obtaining custody. I would recommend requesting the appointment of a guardian ad litem. A guardian ad litem is an attorney who represents the best interest of child and is able advocate for the child. They can do inspections of each home, speak with doctors, counselors and other professionals. The guardian ad litem can then submit a report to court and testify on behalf of the child. I believe this will be a key to victory.
I hope this information is helpful and I wish you the best of luck.