Praise be to Allah.
The mahrams through marriage fall into four categories:
1.The ascendants of the husband [his father and grandfathers] become mahrams to the wife.
2.The descendents of the husband [his sons and grandsons] become mahrams to the wife.
3.The ascendants of the wife [her mother and grandmothers] become mahrams to the husband.
These three categories become mahrams as soon as the marriage contract is done.
4.The descendants of the wife [her daughters and granddaughters] become mahrams to the husband. In this case there must be consummation. Once consummation takes place, then her daughters from a previous or subsequent husband become mahrams to him forever.
End quote from al-Sharh al-Mumti’ (12/128).
Thus it is clear that there is no relationship of mahram between the ascendants and descendants of the husband, and the ascendants and descendants of the wife. The husband’s mother is not a mahram to his wife’s sons, so it is not permissible for her to shake hands with them or be alone with them or travel with them.
And Allaah knows best.