I’m so sorry to hear about your mother.
The purification offering you’re referring to is the Mourner’s Qaddish, a prayer that devout Jews pray for eleven months after the death of a parent (other immediate family for thirty days).
Since you are a Catholic praying for your Protestant parent, I recommend you use a Christian prayer for your mother, such as the rosary or the Divine Mercy chaplet. However, if you wish to say these prayers for eleven months after the pattern of Jewish prayer for the dead, that is fine.
You can also have Masses said for her. Along with the Eucharistic sacrifice, the Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead (CCC 1032).
God bless you.