Spiritual healing refers to healing of the wounds that separate us from God which are the result of sin. God heals those wounds through the Sacrament of Reconciliation, when we repent from our heart and resolve to change our lives.
Mental/physical healing deals with fear, anxiety and despair. This requires interior healing of the memory. If traumas of the past are not dealt with consciously they can affect our present lives in a negative way.
Jesus said to the paralytic who was brought to Him in a stretcher through a hole on the roof: "Courage child, your sins are forgiven". He did not tell him get up and walk first. Jesus is teaching us that there is a connection between our mental inner healing and our physical healing.
God sees our present, past, and future. When we pray for healing of our family tree. God touches those who are on this earth and those members of our families yet to be born. Jesus can enter into our family tree. He can heal what causes our families to suffer. God is not bound by time. There is no time with God. Christ in the Eucharist has the power to heal every family tree. We need to repent and ask the Lord to break the chains of sin.