Can the custodial parent be ordered to pay for some of the cost to get the child to the noncustodial parent?

I would try something. Why don't you try for custody of your child? My x and I live about 50 miles away from each other and most of the time, we either meet half way or I'll take them to his neck of the woods and he brings them home. That way, each of us only makes one trip. You aren't being fair to your child when you cancel on him.