I'd advise that first and foremost the dad tries to see this throught the eyes of his son and tries to overlook his own hurt.
I imagine that the 3year old DS was incredibly hurt when his dad was no longer there all week - especially because his son was so used to having special and enjoyable times with his dad.
At 3 he is too little to understand that his dad has probably done this for the good of his family. For a three year old a week lasts forever and a weekend is over in a flash. He feels abandoned and confused.
His dad needs to take it on the chin. It must be very very difficult for him but he needs to avoid putting any guilt on his son about this rejection - no 'don't you love daddy anymore' type questions.
I think the dad needs to let his son know that it's ok for the DS to be angry and confused and upset - his world has been turned upside down by this.
To put it into context, my DD aged 3 couldn't cope with the knowledge that her dad was going out the other night and coming home on the last train. She was upset because she knew he wasn't going to be in the house when she was asleep - even though she knew he wouldbe there in the morning. Yet at 2.6 years she happily kissed off on his way to Dubai for 10 days and waved at aeroplanes in the sky which she believed he was on.
Probably if this had happened when he was 2 the fallout would have been considerably less, but as with my DD aged 3, they seem to be less able to cope with change at this age. They also have a wider but still limited understanding of distance.
I suggest that the parents remove any emphasis on the dad and DS having 'special time' together - the dad has temporarily forfeighted this right imo, unless the DS specifies that he specifically wants to spend time alone with his dad (unlikely).
Perhpas his DS feels insecure around his dad and might even have separation anxiety throughout the weekend that over shadows the time they have together. He might only feel truly safe when his mum is there because he doesn't expect her to leave him. Mum is the constant and he doesn't feel abandoned by her so it's natural for him to want her to be his main carer.
I think the three of them should spend all the time together. It's irrelevant now that the dad and DS had hours of fun playing trains together - all that matters now is that DS needs his dad and mum to play trains - the three of them together in order that DS can feel secure and safe.
The dad needs to build up his son's trust - if he doesn't want his dad to bath him - suggest that the dad helps the mum bath him. That son sits on mum's knee whilst dad reads the bedtime story, or that DS sits in between mum and dad and they take turns reading a page each of the story.
Whatever happens the DS should not be made to feel that he is being silly/selfish/difficult about this behaviour and neither parent should force the issue IMO. Progress will come but at the DS's pace and with patience and understanding of his parents.