All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad (sallallaahu 'alayhi wa sallam) is His slave and Messenger.
Your wife has no right to demand that you divorce your second wife, and it is not permissible for her to request that you divorce her so she may have you all to herself. It has been narrated on the authority of Abu Hurayrah (
) that the Messenger of Allah (sallallaahu 'alayhi wa sallam) said: “A woman must not ask for the divorce of her sister (i.e., co-wife) in order to overturn what is in her container.” (Imam Al-Bukhari)
Furthermore, you are also not required to comply with her demand simply because she promised to respond to you sexually if you did so. One should know that it is forbidden for a wife to refuse her husband in bed (sexual intercourse) without a legitimate excuse — such as illness that would cause harm, or if intimacy prevents her from performing an obligatory act.
Lastly, we advise you to deal with her wisely and kindly to preserve harmony, and to be diligent in showing justice between the two wives in terms of overnight stays and financial maintenance. However, if she becomes rebellious (nashiz), then her right to maintenance and overnight stays is suspended until she returns to obedience.
Allah Knows best.