It sounds as if they are making too big an issue of it and putting too much pressure on him. I know it feels like the natural way to behave, but it isn't helpful.
My daughter was like this; wouldn't poo in the toilet for a good 18 months. She would poo in one place only, and at one time of the day - always in a nappy.
First thing I would say is to ease off - all three of them in the loo trying to get a result is too much. They get stressed, he gets stressed and it's no good for anyone. It often starts as a control thing - it's the only thing he can really control for himself at the moment. So we found that letting dd ask for a nappy and then letting her get on with it helped - she would take herself off in private once a day.
Tell him that he can ask for a nappy for a poo, or give him one when you think he needs one, but don't stay with him and keep on at him about it - let him take it away and deal with it himself. Don't force him to use the toilet if he doesn't want to.
Don't make a fuss, don't get hysterical, don't make him feel as if his poo is the be-all and end-all of everything, and definitely don't punish. Even bribery doesn't work when the fear of the toilet is as bad as this.
My experience is that lactulose won't help - it doesn't soften the poo enough to mean that he won't be able to hold it in. It can also take a couple of weeks before it starts to have any effect and needs to be taken long-term in most cases. Sometimes we resorted to Califig (a laxative) which always got us a result pretty quickly - like your nephew, dd wasn't constipated, but we needed to get her to the point where she just couldn't hold onto it, and Califig did that.
They need to take the pressure off - don't force him. Maybe see the GP for some Movicol, and consider Lactulose in the longer term. If they tell him that he can always ask for a nappy, and then leave it at that, it puts him back in charge (which, of course, is what it's all about).