I'd contact her employment agency and let them know... Whoever you had to sign up with for care. They probably did not tell her about the snake or she didn't read the info they gave her. In either instance, it needs to be reported to prevent it from happening in the future. They also need to know that your father did not receive care. If you pay for that care, they need to remit the cost of that visit. If your insurance pays for the care, still contact them and tell them that you need to have a makeup visit to compensate or you will contact your insurance agency and report the incident, etc.
The women did act unprofessionally and although people can have serious irrational fears, she should have come back after the freak out to at least explain and schedule someone else to come and do the appointment if she was literally that afraid.