Your mother cannot petition for a minor child until after she receives her green card. If the child is on a tourist visa, he must return to his country of citizenship before his I-94 expires. If he is not legally present, he must return home. There is no way your brother can remain in US while awaiting any immigration visa.
Your mother must earn enough to support self, all dependents, plus the person(s) she sponsors. She will need her current year paystubs, and her last 3 years of US income tax returns. If she is awaiting a green card, she must have been on some status (e.g. employment visa) which allowed her to legally work, or else she's going to start looking for a job only after she obtains a green card. It could be quite a long time before she's earning enough to sponsor anybody's immigration. What's going on with that?