No, you do not.

Your mother also sounds like there is some early dementia that could be going on.

Do not take her in.
Do not liquidate any of your assets to assist her financially.
If she wants to hang on to her house, let her, she will end up dying in it.

If you have to disconnect, do so. Do not enable her to continue living at home. When she brings up her health, tell her she should look into assisted living. This will probably keep her quiet.

When the inevitable medical crisis occurs, if she calls you tell her to call 911 and let them handle it. Don't sit in waiting rooms waiting. If the hospital calls you to come and get her or implies she will be coming home with you, YOU WILL NOT DO SO. TELL THEM SHE IS UNSAFE TO LIVE ALONE AND NEEDS PLACEMENT. Then have the social worker at the hospital do that.

Let me find a message board I used to participate on, it dealt with sick toxic relatives.

ETA: here it is: http://mikegamble.websitetoolbox.com/