Is a wife to whom it was said, "You are unlawful to me," considered unlawful to her husband, bearing in mind that this was said to appease the other wife?

What your wife did, asking for the divorce of your other wife, is impermissible, as it is definitively prohibited. Regarding your statement to your wife, "She is unlawful for me (haram 'alayya)"; if you meant that she was unlawful for you at the time of uttering the statement, then this is a lie and does not necessitate a divorce. However, if you intended to make her unlawful for you, then your intention must be examined: if you intended divorce, then it is a divorce, and you may take her back before her 'iddah (waiting period) expires, provided this divorce does not complete the three divorces. If you intended zhihar (a pre-Islamic form of divorce by likening one's wife to a prohibited relative), then it is zhihar. If you intended an oath by Allah Almighty, or if you had no specific intention, then an expiation for an oath (kaffarat yamin) is binding upon you.