What the child states is not relevant to the court. There will be no custody battle as your wife already appears to have primary physical custody, what the father is requesting is his visitation. If it's in the order that he gets the entire summer, not sending the child will be considered custodial interference, and if he presses the issue your wife could find her custody status being changed.
I get that the child has issues with spending time with what has been an absentee parent. Even if the absenteeism was due to deployment, it still meant he wasn't around, and sending a child for an entire summer is likely scary for both the child and mom. What you can do is to try to do a gradual step-up of shared time prior to the long term trip in the summer. Give the child a chance to get used to dad being around.
If dad is unagreeable with this, you can attempt to go to court in SC to require reunification counseling. SC is the court that matters since that appears to be the childs legal residence.
Honestly, though, if dad isn't a proven child abuser your wife is going to be better off trying to demonstrate she is supportive of their relationship. Calm the childs fears as best as possible, setup a time for skype during the visit, and deal with behavioral issues when he returns. After the first few days the child could adjust if given the chance.
Family court judges have seen everything - every excuse, every type of situation, and heard every fear you could imagine. Your wife will need a major problem in order to get a judge to interfere with an ordered custody arrangement.
Marriage doesn't come with a money-back guarantee.