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I am sorry to hear about this situation. The Court decides on custody based on the rule of thumb of "best interest of the child." This includes, but is not limited to, general stability of the parent, financial stability, indoctrination of the child in the current school and environment, household condition and living condition of the child, other persons living in the house, etc.
IF he is convicted of the DUI and/or the assault, one's chances of being named the primary custodian would likely rise.
His convictions may also limit his visitation. One parent usually becomes the custodian and the other parent becomes the "visiting" parent which is generally one day a week, every other weekend, and alternating holidays. The nuanced points of the custody can either be decided by the parties or the Court, if the parties cannot come to an agreement.
Even if a parent does not get managing custody, they are almost guaranteed visitation unless they have a drug problem, alcohol dependency, or an unsafe home environment. Abuse and or neglect of the child or previous children are an almost automatic bar for even visitation, although supervised visitation may be granted by the Court.
Of course, that is the standard order of possession. That order can be modified if both parties agree or if the Court finds that it is an extraordinary situation.
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