can my 78 year old US citizen mother file for a 53 year old divorced daughter?

The mother can file an immigrant visa petition on behalf of her daughter. Her daughter will have difficulty obtaining a green card. The daughter will not be able to seek a green card in the United States unless grandfathered under INA 245(i). The daughter will need to reopen the removal proceedings. Otherwise, she will require both a waiver for unlawful presence and application for permission to reapply for admission after removal. This is a complicated matter. The mother and daughter should meet with an attorney to understand the process involved. In the interim, you can read more about family immigration at http://myattorneyusa.com/family-immigration.