Agreed if it is there dog entering your property, then the fault lies with them...
i wouldn't pay any second vets bills etc. just tell them nicely to keep their dog of your property as you cannot be responsile for what happens if they do enter your property...
Snap.
Neighbours fault for not looking after there own dog ,,, if my dogs wandered into someone else's garden or the road or out the garden in any way i would make sure it didn't do it again by securing my side not your problem if they are irresponsible ,,,