Is money earned from training, which was subsequently acquired, and which was obtained on a day I went out with a worker using my car, permissible or impermissible (halal or haram)?

The intent of the question is unclear. However, if the question means that the company pays the employee a transportation allowance for training, then there is no harm in taking it, provided the company's conditions are met, as the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." If the money is a trust intended to cover specific costs, then any excess beyond what is needed must be returned to the company. But if it is a lump sum from which no remaining amount is required to be returned, then the employee may benefit from the remainder. If transportation is by private car, what the employee is entitled to depends on the company's conditions.