I'm going to deny my mother a place to recuperate
I'm shocked. Why would you do that to your mother?
She is a liar, she never even thanked me for taking her to her house.
She probably forgot to thank you! You should still care for her because she needs it! You should always try to help family in their time of need.
She's my enemy now. I hate old people.
She has helped you grow up and she's a member of your family  so I suggest you forgive her and try to communicate to her that lying is wrong so that she would understand. Even if you have no responsibilities of taking care of her, she may not have anyone else to do the same and she may only have you.