What is the age when court considers the opinion of children? How?

There is no age when children decide. If a guardian ad litem is appointed, the child can express his opinion to the guardian, who can then reflect it in the report. You don't say why the boy doesn't want to go to his father? If there is a problem there and he won't tell you what it is, I suggest you take him to a child therapist where he can talk to a neutral person who can either help him deal with it or provide information about why it's not in his interest to see his father at this time.

There is no set age. A court (usually through a guardian ad litem) will hear about the child's preferences, but they are not binding on the court. The question for the court is the child's best interest. Courts often discount reports of a child's crying and demanding to go home to one parent while visiting the other. Separation is hard for many children (and adults too), and there could be the suspicion that the parent who says the child is crying may be alienating the child from the other parent. Also children are often wiser than their years in their capacity to manipulate their parents. You can have your lawyer move the court to change placement if you have legal grounds acknowledged in your state.

You have a duty to encourage dad's parenting time. See an attorney with details.

This can get a little tricky as to what is meant by "when the court considers the opinion of children". The court can, if it chooses, give greater weight to the opinion of children 14 years of age or older, but the court is never under any obligation to craft a child custody order based upon the expressed desires or opinions of the child of any age. See Utah Code Section 30-3-10(1)(e).