In regard to threatening suit and negative commentary, the approach is definitely aggressive, but they have renegged on their agreement to cover the additional costs. It is their malpractice and now breaking their word that you would be commenting about. They are the bad guys, not you. The pressure is what you are going for.
In regard to the breach of contract claim in small claims court, often times the court will say that this really is just a repackaged malpractice claim (which is true) and dismiss it and only allow you to go forward on a malpractice claim. So there is some risk in pursuing a law suit without an expert. If you subpoena
your veterinarian, then he has to show up or will be in potential contempt of court. The court won't dismiss your case when you have a subpoena outstanding. Nevertheless, the veterinarian could simply give you bad testimony and refuse to call the other vet's acts malpractice. This is because most doctors won't testify against another doctor unless they are being paid for their opinion in some way or another.
So, if you are not prepared to hire a malpractice expert, then filing suit does carry risk of having the case dismissed with costs assessed against you. Nevertheless, the threat of filing suit is often enough pressure to achieve your goal. Even if you don't end up filing suit, this should not stop you from threatening to in the demand letter.
In the end, the only way to force them to do the right thing is to sue them, so that may be your only recourse if the pressure you apply with the letter does not work.