Is the mother's boycott of her son's in-laws—on the pretext of her disapproval of the marriage that produced two children—considered a severance of kinship ties?

The general rule is the impermissibility of abandoning a Muslim for more than three days, unless there is a legitimate شرعي reason, such as innovation in beliefs (bid‘ah), open defiance in committing sins, or causing harm. This is based on the Prophet's (peace and blessings be upon him) saying: “It is not permissible for a Muslim to abandon his brother for more than three nights. They meet, and this one turns away, and that one turns away. The best of them is the one who initiates the greeting of peace.” Maintaining communication is particularly emphasized for neighbors, in-laws, and relatives, and they should hasten to reconcile, as stated in the Almighty's saying: {and reconciliation is best} (4:128) and {The believers are but a single brotherhood, so make reconciliation between your two brothers and fear Allah that you may receive mercy} (49:10). If the in-laws maintain contact with the mother, and she insists on severance, then they are absolved from the sin of abandonment, and she bears the burden of sin. We also note that if the mother has no blood relation to the in-laws, then abandoning them is not considered severing ties of kinship (qati‘at ar-rahim), but rather a mutual abandonment between Muslims, which is forbidden without a legitimate شرعي right. We also note that a brother's obedience to his mother in choosing a wife is obligatory, unless it leads him to disobey Allah. If he marries, then he must strive to please her, show filial piety to her, and treat her kindly.