If you were never married and there hasn't ever been an adjudication of paternity, then the father has few rights and under Arkansas law the mother has custody unless and until a Court orders otherwise.
That means you can put limits on visitation. If you do not believe it is in your son's best interest to go on an out of state trip with his father (which would be reasonable if your son does not recognize him). You could actually deny him all visitation -- but it would be best for your son to try and encourage the father-son relationship by trying to work out reasonable visitation arrangements.
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