What about ringing a cat behaviourist and explaining the situation and ask for some professional advice ?

I don't think asking her to keep her cat inside would be helpful, to keeping communication open between you and your neighbour.

It IS early days yet but I feel professional advice is the way to go.

PS. Ring some local shelters most have links to behaviourists etc. I found a feline behaviourist who gave us free advice over the phone via our local RSCPA

Good Luck and I hope things improve.