Is it sufficient to ask about one's mother over the phone and avoid visiting her at another son's house due to that son's behavior, knowing that the mother lacks nothing and all her needs are met?

The mother's right is great, and honoring her is one of the most obligatory duties. All her capable children must spend on her, serve her, and care for her when she is in need. It is not permissible to abandon visiting one's mother without an excuse. Therefore, if there is no harm in visiting her at her brother's house, and it is not possible to visit her elsewhere, then it is not permissible to stop visiting. Dealing with a person whose wealth is mixed (lawful and unlawful) is permissible if the unlawful portion does not predominantly constitute his wealth.