Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
You have a right to ask for a separate living quarter, and your husband should provide the same for you if he can afford it.
You also have a right to your time with your husband; duty towards one’s parents in no way means depriving you of your rights.
Islam teaches us to balance our responsibilities: The Prophet’s words should guide a Muslim to do so: “Your body has rights, your eyes have rights, your guest have rights, your spouse has rights.” (Al-Bukhari)
Therefore, your husband ought to balance the rights of parents with those of his wife: he cannot sacrifice one for the other. In other words, he cannot say: Since I must honor my parents, I am allowed to neglect my wife. If he persists on such behavior, he is guilty in the sight of Allah.
I would urge you to ask for your right to privacy while being respectful of his parents and supporting him in taking care of or serving his parents.
If nothing works, then you may need to reconsider your relationship; he may not be a person who can balance his spousal duties with his duties towards his parents.
It is hard for such people to have a successful marital life.
You may do well to study together with the book entitled, Blissful Marriage: A Practical Islamic Guide by Ekram Beshir and Mohamed Rida Beshir.
I pray to Allah guide both of you to act rightly and preserve your marriage.
Almighty Allah knows best.
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