From the description of this family unit, I would recommend the use of Bowenian family systems, also known as "Intergenerational Family Therapy". It seems that since the death of her Husband, Janet's mother has been unable to express her emotions in a healthy way. Taking out her emotional turmoil on her grandchildren, she seems to be inadvertently causing anxiety and self-doubt in them. Intergenerational Family Therapy focuses on how the values, thoughts and experiences of each generation effect the next. Bowen's theory centers around the togetherness and individuality. Emotional processes that continue throughout the generations can cause conflict, or cause the nuclear unit to develop emotional problems. It sounds that Janet's children are experiencing a reactive distancing because of their grandmother's criticisms and emotional issues. I feel that for the overall health of the family, all members should be involved in the therapeutic process, Janet, her mother, the boys, and their father. Family members would meet individually and as a group for multiple sessions. Relatively equal participation would be expected from the members of the family. However additional meeting may be necessary with the mother and her two sons, separately or as a unit to ensure progress with the emotional withdrawal issues. Certainly additional meetings would be needed with the grandmother. Assessment tools utilized would include those outlined by Conoley and Conoley (2009). I would expect the outcomes of intervention to be lowered anxiety and emotional turmoil, differentiation of family members, and the building of stronger relationships between members.
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