The clinic where I had my dog spayed caused a problem that resulted in the dog needing a $1,400 operation to save its life. I had a different clinic do the surgery since I no longer trusted the first clinic. The second clinic said the first definitely screwed up royally, and would testify if need be.
Veterinarians, just like physicians, can be sued for malpractice -- and many of them have malpractice insurance. By all means demand that the first vet pay for the damage he or she caused. Putting your demand in writing is the best way to be taken seriously. You are extremely lucky to have found the second vet -- on a number of levels. And Vet #2 might just provide the extra oomph you need to make Vet #1 take you and your claim seriously.
If you do not get a satisfactory answer in your negotiations, consider small claims court, where you can sue without a lawyer. For help in drafting your demand letter, and in preparing and presenting your small claims case, see Everybody's Guide to Small Claims Court (Nolo).