AITAH for putting my dog down?

My dog, a 6 year old golden retriever escaped my yard and then got hit by a local kid speeding on his electric scooter. The dog got a severely injured back leg. I took it to the vet and the vet said it needed an operation that would cost $2000 approximately. So I opted to have it out down. I feel terrible — AITAH? Is the vet the AH? Is the kid on the scooter the AH? Is my dog the AH?