Is it obligatory to avoid taking money from siblings if there is doubt about its source due to their failure to adhere to work schedules, and is it permissible to inform the mother to advise them without incurring her anger, and is it permissible to take money from them again if their work improves?

The employee must adhere to the work contract. Lateness without an excuse or permission is not permissible, and its حرمة (sacredness/prohibition) increases with lying and deception. He is prohibited from a portion of his salary commensurate with the dereliction.

It is necessary to advise the brothers and draw their attention to this matter. Informing the mother should be done with consideration for the overall benefit. If the brothers cease their actions, there is no need to inform her. Otherwise, informing her is permissible.

As for taking from the brothers' money in the event of their dereliction of duty, it is not impermissible, because what is impermissible from their salary is only that which corresponds to the dereliction of duty. There is no harm in refraining from taking from their money if that leads to them abandoning their dereliction of work.