Trying to get "sole custody" is an uphill battle and the courts are loath to give a parent exclusive parental responsibility and time-sharing. Be realistic and recognize that unless it would be in the child's best interest not to do so, the court will not give you "sole custody."
That being said, you should subpoena the hospital and medical records, not to mention any police reports. You may need the court to give you permission to subpoena such records. You can subpoena the individual witnesses or you could subpoena the custodian of records. Either could work.
This is not to be considered legal advice nor does an attorney-client relationship exist.