Once the FIR has been registered, police gets statutory powers to investigate the case and the courts will not interfere with the investigation. Lower courts have no power to interfere in the investigation. Only the high court can sometimes monitor the investigation and give directions during investigation, but that happens in very rare cases and not in a routine manner. If you have very strong material to show injustice, you may file a writ petition in the high court, but the chances of the high court interfering in the investigation would be very less.
What perhaps can help is approaching the senior police officers, such as SP of the district. If convinced, senior police officers can ensure proper investigation in the case, including application of the correct sections of law. You can show the evidence to the senior officers.
Once the investigation is over and a charge sheet is filed, the court can direct further investigation and if needed the court can frame charges under different sections if there is evidence to support such different sections, as mentioned by you.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.