How to stop relatives from using Mom's bad memory to manipulate her?

Don't keep reminding your mother of the bad stuff. It is more important that she enjoys the company of her niece? nephew? and her daughter - even if you personally feel that she does so on false premises.

The thing is, the sneaky things these people did to take control of your mother's life were, QED, unsuccessful, were they not. You, however, successfully took control of your mother's life and moved her in with your husband and yourself. Your next step is to gain guardianship of your mother on the grounds of her loss of capacity. Since you are claiming that she is unable to make sound decisions because of her short-term memory loss, you cannot at the same time claim that she has the necessary capacity to give you power of attorney.

I have to say this. While I understand your anger with your sister's and your cousin's exploitation of your mother, and your fear that they might continue to take advantage, I repeat that the taking control appears to be being done by you. It isn't just a matter of where she lives, it's also your determination not to allow her to think well of them or to "be loving" with her own daughter. Your deceitful, manipulative sister is still her daughter. Don't deprive her of that.

Both the Durable POA and the Health Care Proxy are revocable documents. If a relative is intent on taking mom to a lawyer to create new docs, there really is nothing you can do to stop that from happening. However you can have these documents revoked and new ones created so long as your relative is still legally competent. Also once your relative has a diagnosis from a physician of dementia, you need to ask the doctor, in mom's presence, if the doctor believes mom is no longer competent. If the answer is yes - get it in writing. That written opinion can help you challenge any document(s) created after the opinion letter or help you apply for guardianship through the court. I do not suggest you create documents or apply for guardianship without the assistance of an elder law attorney. This is complicated.

You seek Guardianship to protect the finances and health of Mom.
You also bite your tongue and withhold any criticism of her visitors. For what little time she has left, let her enjoy their attention lie a warm sunny day.
Address their errors to them, privately and not in her presence.

If she still knows what is going on a Durable a Power of Attorney and a Health Care Directive completed by an Elder Law Attorney will address her wishes. Since she lives with you you can limit their access to her accounts. I would get the documents completed and work with her to address her financial and medical wishes and then allow her to visit with the family members socially but then you can stand up to them saying the other issues are handled. If you don't feel that you can stand up to them the attorney can help you find a Professional Guardian or POA but it does cost money to pay professionals.

If you have POA and your mother has clarified her health care wishes, preferably in writing, and all the legal paper work has been completed...then you don't have anything to worry about in that regard. From my experience, similar to yours, my only comment would be it's a good thing that you've had this time to figure out the relatives and their intent, before some decisions have to be made for your mother because she is incapable. You have received a forewarning. In my case...when some important medical decisions had to be made about my mother's care, my sister and my manipulated father, did some things under the radar, which IMO cost my mother her life. Decisions based on my sister's skewed opinion. Didn't find out about it until it was too late...after my mother passed. If I knew then what I know now, I would have fought for my mother. Had no reason at the time to think my sister was so devoted to her opinion that she would let it overshadow her decision making, good judgement, and then lie about it.

You know, from your report here, what these relatives are capable of. Keep your eyes and ears open when they are around. But, don't prevent them or your mother from seeing one another. For what it's worth...

Oh how I can relate to what she post:/ the way I see it every dog has their day and the manipulator will get there's when they least expect it! I know my reply may not help but I needed to vent myself.

No lawyer in their right mind would change anything if you already have POA. If your mother has a lawyer call them and explain things to them. There is no sense in reminding your mother because she will only get upset and then forget anyway.

Countrymouse is on the mark-- be wary of projecting onto your relatives what you might fear they are thinking of you. Keep in mind that this is what dying of old age entails. Therefore, never argue with or remind someone with short-term memory loss or dementia issues of negative moments. The stress of struggling with day-to-day tasks, the confusion and frustration are difficult enough without needing to recall painful memories. This can augment fears and latent anxieties. Let her spend her final days in warm fuzzy memories, positive interactions, and peace. At 95, she deserves nothing less. I certainly want my children to do that for me.

no unsupervised visits seems to be easiest way. If they ask to visit at a time you are not able to be there - just say "That's not a good time and suggest a time when you can be there" Lock up the check book/credit cards/ and legal documents.
Be sure you have her Trust/will - POA - Health Care POA, etc.
If they are up to no good (been there done that) they will disappear soon enough when there is nothing to be gained.
If they are truly there just to see your Mom they can surely understand that a short visit will make her happy without tiring her out.
You are the one who has to deal with any negative stimulus they cause (after they leave) since she lives with you and you are providing care. That means you call the shots as to what keeps Mom happiest.
Visits are great - you don't need to explain anything to Mom (she will forget)
Let her enjoy the company -
Just keep an eye on family as you would anyone who is dealing with your impaired Mom

What "sneaky things" have your sister & cousin done to "take control" of your mother's life? Have they done these things after she moved in with you?

How do they "manipulate" her into things?

If you were more specific about the things that they have done, it might result in better feedback from members of this site.