All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Allah the Almighty has permitted the Muslim man to marry up to four women as long as he observes justice and equality amongst them with regards to maintenance and sleeping over. Thus, if a man wants to have a second wife and be committed to giving both of them all their rights stipulated in Sharia, then this is permissible. This is unless the wife stipulated in the marriage contract that he doesn`t marry another. If this is the case and the husband didn`t honor this condition then she is allowed to ask for dissolution of marriage and claim all her marital rights. This is because there is a benefit for her in this condition and it doesn`t contradict with the requirements of the contract. The Messenger of Allah says: "Muslims stick to their conditions as long as they agree with what is true." {Related by Al-Hakim}.
Article (A/37) of the Jordanian Personal Status Law states: "If the wife made a condition in which there is a lawful benefit for her and it doesn`t infringe upon the rights of others, such as not to take her abroad, not to have a second marriage (husband), not to reside in a certain country, not to ban her from having a job or that she enjoys the power of Talaq/divorce, then this condition is valid. In case he didn`t abide by this condition, then she can ask for dissolution of marriage and she is entitled to claim all her marital rights.
However, if the promise was delivered verbally and haven`t been documented properly then it is just a promise which doesn`t grant her the right to ask for the dissolution of marriage. Nevertheless, a Muslim should keep a promise, and the Messenger of Allah (PBUH) told that not keeping a promise is a sign of the hypocrite. Narrated Abu Huraira: Allah's Messenger (PBUH) said: "The signs of a hypocrite are three: Whenever he speaks, he tells a lie; and whenever he promises, he breaks his promise; and whenever he is entrusted, he betrays (proves to be dishonest)". {Related by Bukhari}. And Allah the Almighty Knows Best.