I am 41 years old and I am taking care of my grandmother, but for much of mine and my sister's lives my grandmother has always been a negative and nasty person and it's gotten much worse since my grandfather and mother had passed away. She's saying things that are inappropriate and often times abusive and has done it in front of people. People have said to me "oh she's old she can say whatever she wants" yet they're not the ones who are dealing with the verbal abuse on a daily basis. I notice that many people are faced with caring for elderly parents and grandparents, but what is unfair is the way many of us are treated on a daily basis. My grandmother has been a toxic person all of her life she's not very nice to people and has said things even stuff of a racist manner to people that has driven many not to come around. She even had the nerve to say I should forget about marriage and a family because nobody wants me and I am too old. How long can you listen to that kind of negativity until it becomes wearing on you.
You and your sister know the reality of the situation. Don't worry about opinions of anyone else ... except maybe medical professionals.
She isn't going to change, except perhaps get worse. Make a conscious decision, not just act by default. Do you want to continue to live with her and care for her?
When she makes her nasty comments, just leave the room. No matter what is happening, or if you are helping her in some way - tell her that you will come back when she is in a better mood. Don't give her an audience, good luck!
I'd also consider if your grandmother may have cognitive decline. When people show an increase in being negative, challenging, and nasty, it may be due to some mental issue. Some nasty people get worse and even very kind people can get nasty. I'd explore that, because, it may something that is no longer within her control. Regardless, I'd develop a thick skin or make other arrangements for her care.
Are you expecting some kind of inheritance from grandmother? If so, then, I'd consider how much of her behavior you can take, but, if you need the inheritance, then, I'd try to get a counselor and/or support group to help me cope and stay healthy myself. Caregiving is very hard to do. This could go on for years, depending on her health. I'd work on ways to build my self esteem. You must be a pretty good person to be helping grandmother. I'd be sure to remind myself of that a lot and give yourself lots of pats on the back. Sounds pretty impressive to me. Other people likely see that about you too. That's likely why they pay her words no mind.
Grandmothers are not cats, but the concept is similar. You don't inherit the requirement to take care of someone. I can imagine things were very confused for a while after your mother died. I hope things have settled down a bit and you and your sister can realistically face the question "What is the best for the three of us?" GM is not the only one whose needs and wants should be considered. You and your sister are each as worthy as she is to lead a quality life.
If you leave GM's house, where will you live?
Please watch your own health and that of your sister. Your Grandmother could outlive the both of you, at this rate, and how she acts.
One possibility is to have Grandmother get onto Medicaid [which is different from Medicare].... Medicaid has a program where they will pay for Grandmother to be in a nursing home. I realize this might not be an option as many people don't want to move an elder into a skilled nursing facility. Medicaid will then put a lien on Grandmother's house so that they can be paid back.
A lot depends on what care she needs. If you could answer that, it would be most helpful.
I think you need to detach from this toxic woman.
Can you tell us more about this situation? Are you living together? Her house or yours? Why are you doing the caregiving?
A little more background will result in more realistic answers.