Appreciate your problem, been in the same situation myself.
Would you be able to use her daughter as a talking point, mentioning how sad she will be if the shark gets ill and how much happier she would be with a nice betta to care for (maybe you could show some picture of pretty bettas)? Can't think of anything else that would go in a 2.5 gallon tank and they don't sound like the sort of people that would do any serious upgrading.
Maybe her lfs could be persuaded to take the bala in part exchange for a betta?
I totally agree that you don't want to fall out with your neighbour; that would only mean losing your influence over her (not to mention unpleasantness for yourself and your family). She may not have anyone else to advise her on this, so it's vital that you maintain your position.
As a parent, I certainly don't approve of this idea of doing what you know is wrong so as not to upset the children, I think it is bad for them in the end, and they are much happier when made to consider others- but of course, it won't do to mention this to your neighbour, all parents get very defensive when their parenting is called into question. Better to be eloquent on the charm of bettas, how socaible they are and how it would get fond of her daughter (I don't know any balas personally, so to speak, but I wouldn't imagine they are that kind of fish).
