All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
First of all, we ask Allaah to make things easy for you and to relieve your distress and reconcile between you and your husband.
We, as well, recommend you to do what the mufti advised you to do, which is to reconcile. The family will break up by separation, and the children could be badly affected as a result.
Allaah says (what means): {And if a woman fears from her husband contempt or evasion, there is no sin upon them if they make terms of settlement between them - and settlement is best. And present in [human] souls is stinginess. But if you do good and fear Allaah - then indeed Allaah is ever, with what you do, Acquainted.} [Quran 4:128]
Indeed, you did well as you were patient for the sake of your children; we perceive that this is due to you having a sound mind and reasoning.
Asking for a Khul’ is disliked in Islam unless there is a sound reason for it. The mere marriage of your husband with a second wife is not a sound reason for you to ask for Khul’. Nevertheless, if you hate your husband and you fear that you cannot fulfill his rights upon you, then it becomes permissible for you to ask for Khul’. Please, refer to fatwa 131953.
In any case, you should not ask for a Khul’ unless you consider that its benefit outweighs the harm of separation. It is only in this case that you may take the matter to the authorities concerned with the issues of the Muslims, such as Islamic Centers. For the rulings on Khul’, please refer to fatwa 89039.
Finally, we would like to point out the two following matters:
Firstly: the husband is allowed to marry a second wife provided that he is just between his two wives. Allaah says (what means): {…then marry those that please you of [other] women, two or three or four. But if you fear that you will not be just, then [marry only] one or those your right hand possesses. That is more suitable that you may not incline [to injustice].} [Quran 4:3] Please, refer to fataawa 81469 and84411.
Secondly: Lying is a contemptible and outrageous behavior, and it is forbidden except in some cases permitted by the Sharee'ah, such as the husband and wife lying to each other for a good cause without violating each other's rights. Umm Kulthoom Bint ‘Uqbah said, “I did not hear the Prophet permitting lies for people except in three cases. The Prophet used to say, 'I do not consider the following as lying: a man reconciles between people, he lies just in order to reconcile; and a man who lies in war; and when a man speaks to his wife or when a wife speaks to her husband (in certain situations).'” [Muslim]
An-Nawawi said, “With regard to a husband lying to his wife and a wife lying to her husband: it means showing compassion and kindness and promising what is not obligatory and so forth. As regards cheating or deception in not giving what he is obliged to give or what she is obliged to give, or taking what he is not allowed to take or her taking what she is not allowed to take, then this is forbidden according to the consensus of the Muslims.”
Allaah knows best.