Sister and her husband have created a false reality for Mum to make it appear that I, as her son and Carer, have always been mean and abusive to both her and them and that I am a madman and intent on murdering them all. They are clearly suffering from serious mental health issues and refuse to engage or acknowledge their actions. They have manipulated Mum, the health services and other remote family members against me.
Normally, we would tell the OP to contact Adult Protection Services to evaluate their situation because family members are slandering the OP. APS comes in and makes sure everything is in place and may even have some suggestions and resources the OP can take advantage of. This puts a report on the record in case someone reports the OP to APS. APS will need to follow up which is a good thing.
Do you live with Mom or her with you? Do you have POA?
If she lives with you, ban them from the house. Your home your rules. I don't really like a POA banning family members from seeing a LO but if those people cause problems which upset the LO, then I say ban them. Block them from ur phone and social media.
What kind of health services have u had problems with because they believe ur sister? Really, if a health service thought Mom was in danger from you, I would think they would report it and she would be taken from your care. We call people like this "mandated reporters" and they are required by law to report any abuse.
Does ur Mom have money that Sis feels your spending that should be her inheritance?
What do you want the outcome to be?
If you cannot stop your sister and husband (or can't afford the legal route to this) are you willing to give your mom's care over to them? Or transfer 100% of her care to the govt health service (if that's a possibility in your country)?
Do you want to continue to fight to provide her care and block your sister and husband? This will require reporting and legal action.
We can't give you advice without knowing where you live, what your financial situation allows and what you wish the solution to be.
I suppose I don't expect answers as it's just hard to accept that the system can be so easily manipulated when there is a vulnerable person involved. I would have thought that mental health and safeguarding services would require evidence rather than accepting the word of one adult sibling over another. I recall one occasion when a part time carer who had witnessed multiple incidents of verbal and psychogical abuse reported this to a social worker, only to be told that the report was 'off the record'.
Just good to have a voice really as it seems impossible to be taken seriously when reporting Elder abuse, despite having overwhelming evidence, when those you are reporting are aware you know what they have been up to. I'm in Ireland btw.