Does the divorce issued by the husband with the words "you are divorced" take effect upon his wife while she is pregnant and at her family's home?

The divorce is valid even if the wife is pregnant, and divorcing a pregnant woman is a Sunnah divorce. If this is the first or second divorce, it is revocable (raj'i), and the wife must remain in the marital home until her 'iddah (waiting period) ends. She is not allowed to leave it, nor is her husband allowed to expel her.