What steps should be taken with a father who works in a butcher shop selling meat that may be defective or from dead animals, while he believes he does not sell directly to people but only handles accounts? Is it permissible for me not to partake of this money, and is he considered compelled to this work because he supports a family?

If the predominant business of the shop is selling halal (definition) meat, and your father's work is permissible, even if there is deception by selling carrion (haram (definition) meat) or diseased meat as sound, as long as he does not participate in the deception or assist in it. However, if they sell carrion (maytah (definition)), he should not partake in anything related to it, and he must forbid the shop owners from deception.

If the predominant business of the shop is selling carrion (maytah), then it is not permissible for him to work with them, unless he is in dire necessity and cannot find what suffices his basic needs except through this work. In such a case, it is permissible for him until he finds another permissible means.

As for the ruling on your benefiting from your father's money, it is permissible, because the preponderant opinion is the permissibility of dealing with someone whose money is mixed (with lawful and unlawful), with a dislike that weakens or strengthens depending on the scarcity or abundance of the unlawful in this money. "And whoever fears Allah – He will make for him a way out and will provide for him from where he does not expect."