It is common in Arkansas for custody orders to contain a provision that prohibits cohabitation or having overnight guests of the opposite sex. This is usually qualified by "when the minor children are present" and judges will also often include the appearance of spending the night (such as "I left after the kids went to sleep, but came back over before they woke up.").
If the order prohibits overnight guests of the opposite sex, you would not be able to spend the night while the children are there or your girlfriend would be in contempt of court. If she has custody, that would make it impractical, if not impossible, for you to live there.