As it happens, I came across this site / forum whilst seeing where my daughters video was being posted. I cannot speak about our case as it would potententially be illegal. However, in general terms to answer the question what reason would a court give for banning a child and father being together it's worth establishing a few facts most dads never realise until the light of family courts hits them:
fathers have no rights to their children in law - currently there is a review (FJR) which is recommending making this even worse and including grandparents. so, only a mother will have any right