What can I do to bring my mom back after being deported?

I am sorry but it is exceedingly difficult for a person who has been deported twice to return to the US. At a bare minimum, at least 20 years must pass before such person's return to this country is possible. The 20 year bar is counted starting from the date of the last deportation. Also, if your mother again attempts to return to the US, the 20 year bar clock is stopped and restarts again when she is deported again,

Most likely, there is nothing anyone can do. If you want to be sure, come to my office, and we will look at your mother's case (no charge).

No options to do so at this time. She would appear to be subject to a "lifetime" ban under the circumstances you describe.