It’s because her brother was still living with her. Since their dad remarried and didn’t take either Taye or her brother with him, he had to stay with their mother. Plus I think it was a bit psychological, much like why Cinderella never tried to leave her evil step family. The mother brainwashed her children into thinking they needed her and so had to also provide for her. I hope this helps explain it a little bit.
It's partially because respect and a certain amount of obedience for parents is somewhat hard-wired into the human brain. The other part is a large section of nosy humanity who feel that people need to have a relationship with their family, no matter how toxic the family member is. Taye's mother is such a supremely selfish person that the only way one can have a relationship with her is on her terms, which will be entirely for her own advantage. I have seen families like this (some of my cousins fit this description) and there is always plenty of people to tell the person in Taye's position, "You MUST HAVE a relationship with your mother."
I liked the story, but I just can't understand why they have to keep supporting the mother...