What is wrong with this picture?

There is a time for family and then there is time for the personal relationship. The personal relationship needs to come first and it sounds like he needs to put some time and commitment into that more often. This woman needs to sit down and plan important things for the two of them to do every now and then that only includes the two of them. When this can happen the wife would probably be more content in the time he shares with others. She may even welcome sharing some of her time with them to.

If the relationship is serious he would involve your cousin in his activities with his family. I understand his wanting to help his sister, nephew and mother, but why his brothers' gfs?

Would he let her become involved with his family? That might answer some questions. He also might not be ready for a steady relationship, but does want someone on call when the mood strikes. ( not a sexual reference, but just in general.)

Why doesn't she spend time with him and his familly instead of him doing it by himself? If he doesn't want her to do that then he isn't that serious about her because he doesn't want her getting too involved with his family.