Will the abusive behavior make any difference when we set up a custody and visitation plan?

It could. If you feel the other parent would hurt the baby, you may need to ask the court to appoint a visitation supervisor. You'll have to tell the judge why you believe that's necessary. If they are really dangerous, the court may prohibit them from seeing the baby under any circumstances.

This Q&A was found on Children Need Both Parents : http://www.cnbpinc.org/modules/smartfaq/faq.php?faqid=62