Bunmi Sofola is a very good writer. The two posts I've read that were written by her on Vanguard, have both been very interesting. The recent one I just read was titled "Daughter who took care of her dad’s love-child!".
Can you care for your father's mistress' child? This is a very difficult question to answer for most people.
At that moment you're thinking about how your father has been cheating on your mother and that he has a child with this other woman. Plus, the only reason why you are finding out about this is because the mistress' child is asking for your help financially, as your father isn't taking care of this child.
I would advice that anyone in such circumstance should not make impulsive decisions against this other child. It's not the child's fault that your father cheated. They shouldn't be judged based on your father's infidelity or because you want to avenge your mother.
As a Christian or Muslim, God expects us to show love to one another. It's not compulsory to care for this child for the rest of their lives. Do what you can do to help the child. I really don't have an advice on whether you should be the one to tell your mother about this. Your father should be the one to break this news with his wife.
Thanks for reading. Let me know what you think about this issue in the comments section.