I have been berating my neighbour's mad sister. And I am listening
If your neighbour's 'invader' is her sister then of course she has rights.
Any self-respecting sister would feel obliged to 'help out' in the garden. Then - well it depends whether she is an elder sister or a younger sister.
If younger, then a round clout will do the trick. If elder though, then she has the god-given right to do what she wants in her sisters garden - any time she wants - and bring her cat!