The child was born in Hong Kong to mainland parents. Can my mother apply to settle in Hong Kong?

No, your child is, but unfortunately you are not, and you will have to marry a Hong Kong resident for five years before you can settle down. In addition, when you and your husband are 60 years old, children can apply for you, but they can't have a second child. If you have another child in the mainland, you can't settle there because you still have someone to take care of you.