My answer is, it depends.
I think that parents that work a lot of hours can have a close relationship with their child but they have to make the time they do have with them a priority.
When my DD3 was an infant there was only about 1.5 hours between the the time DH got home from work and the time she fell asleep (it was not because he was working mega hours, he was home by 5:30, it was because we could not keep her awake past 7:00). That entire time he spent with her and they have always had very close relationship.
If the relationship with the son is strained, then there's a problem that needs to be addressed.
Personally, I think the woman needs to find more time for her child and spend less time at PTA meetings, club meetings and her other volunteering activities. It's great the father is home, but apparently isn't solving the problem between the son and the mother.
This woman made a commitment to the child when she decided to have the child and apparently her 30 minute a day of quality time, or less, isn't working.