Could you move house so she doesn’t have your address.
Your eldest dd must realise that if what her gm convinced her had happened then you wouldn’t have your other children living with you.
Maybe one day she will realise just how unhinged her grandmother is and the horrific affect she has had on her life.
If you can’t sue your mother then I would be looking to suing SS /Local Authority for making you go through multiple investigations that they know are lies
I would think the police could prosecute your mother for wasting police time, perverting the course of justice
Malicious communication is another offence off the top of my head. I think it is something along the lines of if the communication is designed to be bullying or a hoax or meant to cause distress
The police need to have some idea of the law and start doing their job. I would start by seeing a solicitor and maybe a letter to both the police and SS about them taking your mother seriously and after so many times investigating and proving these allegations are false they must realise that opening an investigation again and again is looking like they are joining your mother in abusing your family.
If anything their investigations have led to one of your children being put into a dangerous situation as she is now on her own with the person responsible for her abuse being the only family member she had contact with
The stress from these multiple investigations is becoming to look like abuse from SS and the police and is negatively affecting the other children
I would also call out your sister and ask her if the only reason she wants you to not make such a big deal out of this is because if you kick up a fuss her mother could end up behind bars.
Or is it because whilst your mother had you in her line of sight she isn’t abusing her