Insurance Of Veterinarian Neither Denying Or Accepting Liability

Just before Christmas my cat required urgent surgery due to a large bladder stone. I took her to a vet that would be able to see her at the soonest available appointment due to the coming holidays. They performed the surgery, which cost about $3k and sent my cat home the same day. Sadly she still showed symptoms of a urinary blockage over the next two days and we had to take her to a separate emergency vet since it was the weekend.

The emergency vet mentioned my cat still had bladder stones and required yet another surgery. I informed the initial vet and he offered to take her back in the next day, but we decided we didn't want to take her back to the surgeon that got us in this mess in the first place, especially since the emergency vet advised that we let a board certified surgeon perform the surgery to be extra certain this was successful. Unfortunately the soonest appointment they could book was the day after Christmas. Long story short, the entire cost of my cat staying at the emergency vet totalled roughly $24k, which I had to pay out of pocket since I do not have pet insurance.

Fast forward one month later I get a call from an insurance company who informed me that the initial vet filed a claim in regard to my cat's incident. I told them the entire story and they mentioned that I might be eligible for reimbursement if my vet was found liable for negligence.

Today I heard back from them saying that they have reviewed her medical records from both vets and decided that liability appears to be questionable. They are neither denying or accepting liability based on the information I provided them in the medical records. However they are offering to settle in the amount of $17k, with $10k paid out by the insurance and the rest paid out by the initial vet. The initial vet called me and mentioned that I am liable for a portion since I made the decision not to take my cat back to him.

Should I agree to this settlement? I haven't dealt with an insurance claim like this before so I don't really know my options. Also, I live in California.

TLDR: My cat got surgery but came home in even worse condition. Took her to an emergency vet which discovered that the first surgery was not successful. They performed another surgery and now I'm broke. Initial vet's insurance is offering to settle, but not the full amount of damage.