Not sure about Indy, but in Ohio the kid cannot nor can the parent simply decide not to visit the non-custodial parent. If there is a reason why they cannot make the visitation on a single occasion, simply call and reschedule. If the child is of a certain age and has a good reason why they do not want to see the other parent, than it's your job to seek a modification in court.
Part of having the responsibility for custody is encouraging the child to visit and have a relationship with the non-custodial parent. What often happens is that a teenager gets involved in activities that take place on weekends, so seeing the non-custodial parent in another city every other weekend just doesn't work. Judges are usually sympathetic to these problems. The non-custodial parent should be given a copy of the child's schedule and invited to attend any games or events. Perhaps they could spend time together after the game.
If there's abuse, violence, or some other more serious issue that is preventing visitation, than I would urge you to talk to your lawyer and file for a modification. Under no circumstances should your child be put in danger.