Can I remove my child from their state of residence to come live with me in another state?

The best way to obtain legal custody of a child whose parents are separated is to go to court to do so.  Taking a child from their home where they were born and live across state lines is not a good idea legally for you now or in the long run in a custody battle. 

What you want to do is get a temporary order from the court on custody and visitation.  It will be temporary because a final decree will be issued upon divorce.  There are many factors that the court considers regarding custody and not only physical custody is determined.   The bests interests of the child is the common thread in most states.  The court will look at the age of your child, the relationship of the parents and the child, the present living situation of the child, the "home" state of the child, etc. 

It will also matter where you bring the proceeding.  Each state requires that you live there for a certain amount of time in order to bring an action for custody in their state. Arkansas I believe may be 6 months.  You need to seek legal advice from an attorney in the state you plan on bringing the action for a temporary order of custody. This matter is too complicated to address fully here.