This is a very sensitive situation. Do not get exited. Do not take any step to irritate your husband. Kindly inform your husband (through somebody) that you are very angry with him due to the illegal relationship and keep on observation. If he calls you and seeks apology, there are chances your husband leaves her and he again love you in future. If there is no response, then you have to understand that he is not interested on you. Since you have two kids, there is every possibility that he will like you. Make good relation with your mother in law.
Regarding teaching a lesson to the second wife (girl) it is waste attempt. Because the much you harass her, the must your husband will get close to her due to the sympathy and may get aversion on you. Hence, do not take harsh step. Wait for some time and wait. Inform this to your mother in law and sought help from her.