You state you are represented. We are barred from advising knowingly represented people unless the person is coming to us directly (ie, not through anonymous AVVO questions) with the intention of looking for replacement counsel.
You have a lawyer. We cannot second guess him. If you are not comfortable with your lawyer, seek a second (or even a third) opinion. We cannot help you online as we do not have the benefit of all the fact.
I agree with both counsel regarding the specifics.
Speaking VERY generally, there is something of a misconception that catching another parent in prior bad acts will win or lose a custody dispute. It is only one of many factors. The bad acts have to relate to the children who are the subject of the dispute. If the mother is abusive to all children in her care, why haven't third party mandated reporters investigated and removed the children from her care? A parent who flees a jurisdiction to avoid culpability and/or to protect the third child--why hasn't she been extradited back to face the music?
There are SO many questions that are beyond the scope of this general advice board. You may see that there is no simple 10 minute answer to this complex issue.
The information provided here should not be construed to be formal legal advice. The provision of this general advice does not create a lawyer-client relationship. Persons with legal questions are encouraged to seek independent counsel for advice regarding their individual legal issues.