Is it permissible to eat from the money of one's mother if she works in a gambling company, knowing that she helps with household expenses? And does the sin fall away if she is compensated later for the value of what was eaten? And what about eating from this money since childhood?

Working in a gambling establishment is forbidden (haram), and earnings from it are forbidden. It is not permissible to eat food whose source is unlawful wealth.

If unlawful wealth mixes with lawful wealth, eating from it is disliked (makrooh) but not forbidden.

You are not required to repay your mother for what you ate, because it is either permissible or unlawful wealth that you do not own. You are not responsible for what you ate when you were young.

It is obligatory to advise your mother kindly, remind her of Allah, and invite her to repent.