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 is His slave and Messenger.
First of all, it should be noted that if Allah blesses a husband with a righteous woman who wants to get closer to her Lord with supererogatory acts of worship, then this is a great blessing for which he should praise and be grateful to Allah, and he should – as much as possible – help her in obeying her Lord, as this is better for him and for her.
Secondly, the scholars differed in opinion concerning a wife praying voluntary prayers in the presence of her husband. Does she need his permission, as in the case of optional fasting, or does she not need his permission due to the short time of the prayer and the fact that this does not interfere with her husband's right to enjoy her?
In our view, she does not need his permission if her prayer does not deprive him of his right to enjoy her and he is not harmed by it.
Shaykh Ibn ‘Uthaymeen said in his commentary on Riyaadh as-Saaliheen:
"Is prayer like fasting in this regard? It is probable that the prayer is like fasting, and that she does not perform voluntary prayers except with his permission, and it is probable that it is not like fasting because the time of prayer is short, unlike fasting. Fasting lasts for the entire day, while the prayer does not; like praying two units of prayer if it is a voluntary prayer, and it is known that his permission is not required in obligatory prayers. The sounder view is that prayer is not like fasting, so it is permissible for her to pray (voluntary prayer) even if her husband is present [i.e. without his permission], unless he prevents her by saying: I need to enjoy you, do not pray the Dhuha prayer, for example, or do not pray the Tahajjud prayer tonight."
However, it is not permissible for a husband to deprive his wife from goodness unless there is a need, like if he is overcome by desire and he cannot be patient. Otherwise, he should help her in obeying Allah and doing acts of righteousness, because he will be rewarded for that in the like manner that she will be rewarded for acts of goodness.
We do not know how this disturbs him, but if you mean that he may be disturbed by her preoccupation in performing acts of obedience while he needs her [to do something], then it is not permissible for her to perform voluntary worship except with his permission, as we have already mentioned.
If you mean that he may be harmed because of her movements or sound, then if there is space in the house in a way that she can perform her prayer in secret without disturbing him, then she should do so, otherwise, it appears – and Allah knows best – that it is not permissible for her to do what is harmful to her husband. The Prophet said, "There should be no harm nor reciprocal harm." [Maalik and Ahmad]
Allah knows best.