I'd approach it just as you would any tourist visa Nigel. I presume the girl is at school? And that she lives with her family? Schooling and family ties is your starting point for reasons to return. Don't mention the 'family issues'. Point out that its simply a niece, taking advantage of the fact that her Aunty & Uncle live in the UK and have offered her a holiday - chance of a lifetime, you'd like her to have the opportunity to visit again in the future so she ain't about to screw her visa situation up by failing to return on time - besides, Uncle will make sure she's on that plane.