How can my mother and I protect ourselves from my siblings who are against her wishes for me to be her live-in, full time caregiver?

My brother and sister continue to tell lies and make false accusations to APS and post nasty lies on social media about me in order to force me out of my mother’s life out of jealousy and greed. They refuse to respect and accept her wishes and try to make false claims that I have turned her against them, kept her from seeing them, steal from her, neglect and harm her, that I am keeping her sick and unhealthy in order to have a job taking care of her, they try to say that she is incompetent, mentally ill and to far gone in her sickness to be able to recover successfully. Nothing they say is true, I love and give my all when taking care of my mother, but we can’t stop the harassment, even after 9 Visits from APS that all investigations proved them all to be false and my mother telling them to stop they refuse to believe that she means it, that she is a victim and I am controlling her.

We moved an hour away because she wanted to move to a smaller home and they blame me saying I made her move, and took her away from them, they rarely visit her and when they do they end up trying to convince her to sell her house and move into a senior living facility, and another time refused to bring her back , and unless I did what they wanted they’d keep her against her will, which finally brought her home after she begged them too. Time after time when she would go visit for 3-4 days they make up a terrible lie which they would produce fake evidence to convince her that I was committing these crimes against her. They would tell her that out of their love and concern for her, they had to tell her the truth that they discovered I was doing, and because I would deny it not to tell me anything, only that she wasn’t coming back and she wanted me out of her house and not answer any questions or talk to me anymore, just hang up. After days of her phone being monitored I was able to talk and find out that they lied and deceived her, she found out they lied to her and came home. They continue to call her and harass her to get rid of me, if she didn’t that she would end up regretting it once I get caught doing the bad things they say I do, then they stop calling to try to punish her for not doing what they want, then wait for her to forget what they had done, with her age she forgets and it all starts over again. She tries to separate her her love for them and what they try to do to me but each time her heart is broken and after they pretend to be nice to her and she thinks they have stopped and she begins to feel a happiness it begins again and after 4 years it has taken a toll on her heart, she yearns for her children to love and respect her like they used to. She misses them and is so sad that they refuse to accept her and choices.

What can I do to protect her and myself against the scheming and unthinkable things they accuse me of, it’s harder to prove my innocence when there are 2 against 1 and they both backup lie after lie. It is emotionally draining for my mom to have continually confirm my innocence, it has worn on her and there are times she just wants them to stop and if she just agreed then maybe they’d stop. It’s hard watching her heart take such a beating, that I to myself think of just giving up and leaving for it to stop hurting her, but know in my heart they would end of putting her in a facility and that would be it. And I just can’t see her having to live like that. So I’m here to make sure she lives in her home for as long as she is breathing.