Only an attorney and the court can really answer the question about how this is enforced in your particular area.
I want to emphasize what Lynn M. posted. Your cousin should be crystal clear that besides his official court-ordered time with his son, he intends to be present for events such as: Parent-teacher conferences at school; school plays, chorus concert, whatever; Boy Scout ceremonies; church events such as first communion or confirmation, if that applies; soccer games or tae kwon do tournaments whatever sport or other activities apply, now or later... In other words, he needs to really think through, with the help of a very good attorney, the level of his involvement in and attendance at events that are NOT on "his time" but are important events in his son's daily and weekly life. And he must know that it works both ways; mom should be welcome at events on "his time" too.
It's possible that the mom could get nasty about dad's turning up at the soccer game or the school play, and you want to be sure that dad's intention to be at these things is clear, if that is indeed what he wants. He and she have to work together for him to know those scheduled things that fall in "her time" AND he must let her know about things she might want to attend that fall in "his time" -- he can't hold out information on her and expect her to give information to him.
He should be certain his attorney is very experienced in custody cases and can answer questions about all this and whether it's a good idea to have these things spelled out etc. Eventually it would be good if the mom and dad can have a civil enough relationship to see each other at events and be cordial for their son's sake.