Is it permissible in Islamic law for a husband and wife to live as strangers in one house, not speaking or sharing anything with each other, and for the husband to refuse any dialogue with his wife?

If the son is discerning and the beating is for appropriate discipline, then the mother does not have the right to prevent the father from disciplining his child. However, if the son is not discerning or the beating is violent, then the father does not have that right.

It is not permissible for the husband to abandon his wife in speech for more than three days. The wife has the right to seek divorce due to the harm inflicted upon her by his abandonment, but divorce only occurs after all means of reconciliation have failed. Mediation is recommended for reconciling between the spouses, and if that does not work, then a balance must be struck between the harm of divorce and the harm of remaining in that situation, in order to choose the lesser of the two harms.