How can a mother be convinced to remove her drug-dealing son from the house, knowing that the father is deceased, and the mother cannot bear to be away from her son, and the brother is causing psychological and social harm to the questioner, hindering his future, and constantly causing him anxiety about the police arriving?

The general rule is that it is impermissible to shun a Muslim for more than three days, unless the shunning is for the purpose of rectification or to ward off harm. If shunning leads to a benefit, such as reprimanding and disciplining the shunned person, causing the general public to turn away from his conduct, or deterring others from committing sins, then it is permissible.

However, if shunning results in harm or has no benefit, then it is not legislated.

As for expelling a brother from the house, if he has a share in it, it is not permissible except with his consent. If he does not have a share, then it is permissible to ask the mother to remove him and to explain the danger of his continued presence to the questioner's reputation and future. If the mother does not agree, then the solution is for the questioner to leave the house.