What is the ruling on taking compensation from the governmental insurance company for a car accident that led to disability, knowing that the insurance is obligatory?

Your father is permitted to take the amount from cooperative insurance. As for commercial insurance, it is not permissible to subscribe to it voluntarily. If it is compulsory and he cannot avoid it, then subscription is permissible out of necessity. However, it is not permissible to take more than what was paid, and any excess amount must be disposed of by spending it on Muslim welfare. Explaining the truth to your father is not disobedience but rather an act of filial piety. If the insurance amount is a rightful entitlement for your father due to the paid premiums and there was no offense committed by another party, then he may take it. However, if there was an offense by another party that led to his disability and the offender's fault is proven, then the offender must pay compensation for his offense, and your father is permitted to take it from the insurance company or any other source.