@ebrown p,
I can also understand she may not want them trampling through her yard (probably through her priced rose brush or some such thing) - to me a compromise would be - if your ball comes in my yard, I will throw it back when I get a chance, but please do not trespass.
That way they try not to get it in her yard, but come on, they are kids and you can't always control the ball - and as long as they are not coming near the house, what the heck is a ball in her yard going to do.
Also, if she continues to act like an old fart, she will be the main target come times like Halloween.