Is shunning a brother who does not pray in congregation, delays his prayers, sleeps through them, and commits sins considered ill-mannered and a severance of kin ties? What should be done towards him? And is obedience to the father obligatory if he orders one to sit with him or prevents one from leaving the house to avoid witnessing his disobedience?

You must advise your brother with gentleness and kindness, and explain the gravity of the sins he commits. If you do that, you will have fulfilled your duty and cleared your conscience, and you will not sin by sitting with him while he is asleep. As for shunning him, if it leads to him abandoning his sins, then it is permissible and not a severance of kinship ties, and you should do what is most beneficial. However, the obligation of congregational prayer in the mosque is a matter of scholarly disagreement. You must obey your father by sitting with your brother for meals and other things, as this constitutes filial piety. Hastening to prayer is recommended, and if you cannot convince your brother of this, you should not disobey your father in this matter.