Is it permissible to divorce a wife who is four months pregnant after the husband discovers she is lying and doubts her chastity and conduct?

You have made a grave mistake and committed a shameful act by testing your wife and having ill suspicions about her, which led to your resentment towards her and your supervision of the family's dissolution. This contradicts Islamic law, which commanded having a good opinion of Muslims and forbade spying on them or accusing them of treachery. Your duty is to repent to Allah, keep your wife with kindness, cooperate with her in obedience to Allah, and teach her matters of her religion, especially prayer. As for her work, if she stipulated in the contract that she would remain in it, then you do not have the right to prevent her, unless her work involves unlawful transgressions such as prohibited mixing or travel without a mahram, in which case you must prevent her.