MURDER CASE: what take it so long for a verdict if the suspect pleaded guilty with the crime

hi> i just wanted to seek an advice.. my grandmother was murdered 4 years ago now,,and still the case is ongoing..her murderer surrendered himself after the crime.. But his family still fighting for the case because they want the case to be homicide rather than murder cause defense said the suspect was mentally disturbed when the time he did the crime.. after four years the mother of the suspect talk to my mom and said they are willing to acccept now whatever the decision of the court neither homicide or murder to close their financial burden.. Our lawyer seems making ways to delay the case.. I wanted to know what is the legal best steps we should make to the case come up to decision now.. is it possible for us to change our lawyer who handle the case from the start since we feel that he is not doing his job properly such us he always come to hearing late so in result the hearing was always rescheduled.. but still we pay him everytime we went to court for the supposed scheduled hearing.If the suspect is voluntarily admitting the crime,is it normal to make the case last for four years now? i would appreciate whatever advice i gain here..thank you..