Sorry to hear about your mother.You may have a claim for negligence and specifically negligent infliction of emotional distress against the doctor who has not signed your mother's death certificate.  Negligence is based on the failure to exercise due care (that degree of care in this case that a reasonable doctor in the same locality would have exercised under the same or similar circumstances) to prevent foreseeable harm.  If the ten day period for the doctor to sign the death certificate mentioned by the funeral home is the period required by law, violation of that statute establishes negligence.It would be advisable to speak with a personal injury attorney.