Can I apply for my mothers green card while she is here with her B2 turist Visa?

If you are a United States citizen and over the age of 21 you qualify to petition your mother.

Yes she is an immediate relative and you can do a one-stop procedure for her. She will need to remain in the U.S. until she gets her travel permit though. If she leaves before then she will have abandoned her permanent residency application. We would be happy to assist in the process. Contact me directly and I will advise the procedures and cost.

If you are a U.S. Citizen you can petition your mother while she is here on a B1/B2 visitor visa. However, the USCIS will question your mother about her intent when she came as visitor - did intend to visit, or did she intent to come here so she could file for adjustment status. While "preconceived intent" by itself is not a grounds to deny adjustment of status by an immediate relative many USCIS officers believe it is and try to deny the application. Also, if you mother recently received or applied for her B1/B2 visa the USCIS may believe she lied when applying for her visa since her intent was to come to the U.S. to adjust her status.