The initial conference date will be little more than confirmation of service of the petition, whether each side is represented by an attorney (or wants to be), and the possibility of assigning an Attorney for the Child. From your facts, it would appear the odds are greatly in your favor to win custody, but there are many more factors which would need to be assessed. As such, I'd highly suggest that you schedule a free follow-up consultation with a NYC Child Custody lawyer.
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If there is a danger to the child, then supervised visitation is an option. Domestic violence, restraining orders and orders of protection are all matters for the judge to know about. An attorney will need to be appointed to represent the child. Have an experienced family law attorney assist you.
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Added to the variables you raise, the position of your children and what they tell the AOC will have an effect, depending upon their age. Prepare all the relevant data for your attorney as soon as possible to construct your case as beneficially as possible, especially in establishing beginning parameters for the judge.
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