Can an attorney, which we did not hire, make a claim for our father against our insurance company?

In Florida a lawyer cannot represent any individual without either written or verbal consent. In the case of an auto accident typical for a lawyer to represent an individual that individual will need to sign an Authority To Represent Contract along with a Statement of Clients Rights. If an attorney has contacted your insurance company or the insurance company of the at fault driver and claims to represent your father and you have not given that attorney consent to represent your father, then you need to let the insurance companies know that attorney does not represent your father.  You also need to contact that attorney and let him/her know that you have not contracted with them to represent your father.