bounty, there is a great review of the vast evidence of the impact of family breakdown on child wellbeing - on phone so can't link, but google Impact of family breakdown on child well being. It is a pdf file.
The conclusion is that family function is as important as family form. So, a high conflict, dysfunctional family will do more damage than a no conflict separated one. It has some good recommendations for how to ease the transition for children.
The other point is that a substantial part of the disadvantage children in separated families have is economic. OECD reports on child wellbeing have found that children do best in countries like Sweden, where there is low income inequality and low levels of child poverty. Sweden has similar levels of lone parents to the UK, but consistently is at the top of comparative child wellbeing tables, the UK does badly, because of poverty and inequality.
My last point, children have always been brought up in lone parent households. It just used to be because one parent would die, or the man would desert, or the state would send large swathes of men off to war. The idea of a stable, two parent household is relatively recent, and short-lived, and there is enough evidence that it was sustained by Valium and depressed housewives.
Did not watch the show, but would question the political and social context it is being made in, apart from anything else.
None of which helps you on a personal level, but you can always post here, whether you are still in or out, there are no conditions. All good wishes, whatever decisions you make 
but I hope the individual counselling will help.