What should the husband do with his wife who stole his money from his bank account to cover the costs of her father's surgery, knowing that they have two children?

If the husband provides his wife with her essential expenses, then her mistake in withdrawing money without his knowledge and lying to him necessitates advising her and rectifying her with wisdom, and clarifying the حرمة (prohibition) of her action. If she regrets and repents, then he must accept her repentance and treat her kindly, for Aisha (may Allah be pleased with her) said: "No characteristic was more hateful to the Messenger of Allah (peace and blessings of Allah be upon him) than lying..." As for the issue of the bank and colleagues, it can be handled by using المعاريض (euphemisms/ambiguities) to avoid lying.