To be honest, the only way I know to secure private data on a free public network is to either have her connect across a secure VPN (complicated and resource intensive)... or to avoid connecting to any web site that requires private data.
Unfortunately free public wifi, by definition, means that data will be transmitted as clear text. Even weak encryption (WEP, WPA) would be preferable to clear text but if it's free public wifi then it's unlikely that this will be available for your mother.