First, keep in mind that sororities and fraternities did not always use hand signs. When speaking with senior members of these of these organizations, I've heard them refer to hand signs, as well as the calls, as a "newer phenomenon". If you were to look at older photos (pre 1970's or older), you will not see hand signs at all. You will see members standing in a group together behind the organization's shield.
The original hand sign used by sorors of Sigma Gamma Rho was indeed different from the current hand sign used. The former hand sign was intended to represent the lower case greek letter Sigma by forming a circle with the thumb & 3 fingers and holding the outstretched pinky horizontally. Some members began holding the pinky up vertically instead. See lower case sigma here:
When members of AKA began using the vertical pinky as their handsign, sorors of Sigma Gamma Rho developed the current official handsign used.
I sincerely hope you will follow in your mother's footsteps and become a part of the beautiful legacy of Sigma Gamma Rho Sorority, Inc. It is indeed a wonderful organization!
Member of Sigma Gamma Rho Sorority, Inc.