Your question is a little hard to read. I guess your question boils down to - do you need to pay for the treatment of a feral cat? Good question and not one that I have had previously. I don't think that I would bother going that route. Your dog and your parents dog attacked a cat on your neighbor's property. Morally, you are liable for the harm caused and should pay for the care. Legally, you could probably make her show proof of ownership, but the fact that she took the cat to the vet is a good first step to proof of ownership on her part.
This is not to be construed as legal advice. I do not have an attorney client relationship with you.
A feral cat is just that - feral, meaning your neighbor does not own the cat. You are not liable for any vet bills.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
IF the cats are feral, they are not your neighbor's property. Therefore, she suffered no loss cognizable by law.
None of which explains YOUR failure to keep your dogs' rabies shots current, which may become an issue as the result of this incident.
The foregoing is for general information purposes and does not establish an attorney-client relationship.