@Mame,
I agree with this as well - but just trying to think of a way to keep the peace. This Uncle I am sure wants to keep in touch with his niece, but unfortunately due to the fact that his niece is a minor he doesn't have a say. If the parents don't want him to be around they can cut him off. Now I think that is stupid.
You know this family best - the mom best. Can you have a heart to heart with her without offending her? I agree with what Mame says but my guess is that in the end - what you really want is to be able to take your niece with you and her friend so this is a pleasant experience.
I guess a lot of this and how you handle it depends on how reasonable the mom is. It would be best to be kind, but honest.
I have two girls and very often one went away somewhere without the other - for different reasons. Yeah I dealt with one whining about how it was unfair her sister got to go to grandmom's house in Palm Desert or so and so got to travel with their cousin. It happens and as a parent you talk with your child - they need to learn that happens sometimes. So personally I am not worried about the younger sister - she will be better served to learn this. And also there can be a world of difference between a 14 and 16 year old - this is likely why they don't get along all that great now (there could be others).
But I ramble - anyway although I agree with Mame - I think it would serve you best if you are as diplomatic as possible.
On the flip side - your niece wants you to be deceitful - it is probably best if you sat her down and let her know that being deceitful is wrong and that it is more likely to bite you back. Maybe all your niece is concerned about is the uncomfortableness she will need deal with at home with her sister. Is it really that they won't let her go or is it that she doesn't want to deal with the uncomfortableness and it would appear to be easier for her if she and you were to lie?