YABU, and a bit smug. But it is odd that they are being asked to look after her rather than the other way round. I sort of agree that they don't need an au pair, but perhaps they need some adult supervision, and constructive things to keep them busy? MN has been full of tales these holidays about children fending for themselves who end up imposing on the kindness of neighbours and friends' parents, and making a thorough nuisance of themselves.
Well I have no idea about their arrangements but if I worked and lived in a city then I wouldn't want my 12 and 14 year olds always being left on their own after school and for the duration of the holidays. If I were a single mum I could probably do with a bit of help wth the cooking / housework etcalso so YABU.
If she's out of the house a lot I don't think it's unreasonable for her to have an aupair to make sure the boys are alright - not necessary "look after" but just make sure they aren't burning the house down, that they are eating properly that sort of thing. If she can afford it, why not?
Having worked as an aupair back in the day, I am sure that the au pair would be quite happy with her own company!