Sally got herself in this mess. How dare she use her mother as a scapegoat.

Jane should write a brief letter to her daughter, stating that she realizes her daughter and family are going through hard times. Tell her her home is open to them, if they ever should need a place. No long explanations or bitterness should be in the letter. A sympathetic tone, could be enough to appease Sally.

No way should she ever plead with her daughter. Jane is the mother, and should never allow her daughter to put her into such a demeaning state.

Jane could send a package to the children, with food, and clothes, coloring books and crayons etc. But, also there,...don't overdo it.

No matter how her daughter decides, Jane should keep up the contact with her grandchildren. They are the link that will eventually bring them all back together.
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A friend is a gift you give yourself.
-- Robert Louis Stevenson