Given your situation as you described, I don't see how a domestic assault charge will have much affect on the custody of your child, unless the charge was based on an alleged offense against that child or another child.
Talk to a child custody attorney in your area as well as a criminal lawyer to deal with the charges.
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It is unclear from the facts if Mother is incarcerated currently. If she is then it is highly likely the court will allow your custody request if there are no other custodial limitations (i.e. drug use, violence, other factors that are not in the best interest of the child). Regardless of the facts, it is the responsibility of the court to make child custody and visitation orders that are in the best interest of the child. It is the court's first responsibility to protect the child and to keep the child safe. If your request for custody and/or visitation complies with these factors you may obtain your requested orders from the court.
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