Should a man continue to supplicate for his divorced wife's guidance so that she may return to him, after he permitted her to travel with their son, or should he marry another?

Your supplication for your ex-wife's guidance is a righteous deed for which you will be rewarded. Your effort to remarry her is better if you believe she is righteous enough to raise your child together. However, if her righteousness is not clear, or if she refuses to return to you, then seek another righteous wife.