Is there any chance of sitting down with her over a glass of lemonade and trying to discuss things like a reasonable person? Ask what she has gaianst dogs. Ask her if her granddaughter could come over for a visit when you would have the dogs on a leash, one at a time, so she would know that dogs are NOT scary? Better for everyone if she knows that.

If not, does she have a spouse you might reason with?

Can you find an exterminator to explain to her where her cockroaches are coming from (as in, not YOUR yard or YOUR responsibility)? Could you get a copy of the laws concerning dogs from your city hall, and mail them to her return reciept requested, so you have PROOF she has been informed of them?

If not, let her know that you are NOT responsible for any body part she place through the hole in the FENCE - a fence is there for a reason, and any adult should know better.

Maybe she's a sad, lonely person, who is just doing this to get attention, like any bored child might do? Get her a hobby - give her a gift certificate to a knitting class or something else to occupy her time and mind!

Just my 22 cents.