The child is not the only person we should be concerned with. That kind of thinking, that women should martyr themselves on the alter of motherhood NO MATTER WHAT is what leads to situations of abuse like this one.

Moms matter too. It does not take from the child to consider the mother.

And let's not forget, this woman IS NOT that child's mother. If you want to consider the child's what about HER children? Should their needs be sacrificed for this child?

This kid is going to have a hard go of it because his/her mother is dying of cancer, his/her dad is a dick, and the rest of the family has abandoned him/her because of what dad did. Forcing caretaking of that child into someone who has clearly said they don't want it is not going to improve circumstances for that child. In all likelihood it will worsen them.

If you want to focus solely on the child, then consider that the child needs someone who will be there wholeheartedly for him/her in the upcoming months and years. Not to experience further abandonment issues because he/she was foisted into yet someone else who does not want him/her.