Is it permissible to spend a lot on raising pigeons from the family's money, given that their income is below average? And is it incumbent upon the children to stand against their father's actions?

If a father's spending on pigeons prevents him from fulfilling his obligatory financial responsibilities towards those he is bound to support, then it is haram (forbidden). This is based on the Prophet Muhammad's (peace be upon him) sayings: "It is sufficient sin for a man to neglect those he is responsible to feed," and "It is sufficient sin for a man to withhold food from those whose sustenance he possesses." However, if he does not fall short in his obligatory expenses, then his spending is not forbidden unless it is extravagant. If his spending is not permissible, he should be advised gently and courteously, without violence or abuse.