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, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
If the husband’s sleeping in a separate bed is meant to desert his wife (denying her right to intimacy), then he should know that it is impermissible for him to desert her without a valid reason such as the wife's disobedience, for instance. You can refer to Fataawa 85402 and 84120 about deserting one's wife and the restrictions to it.
A wife is not disobedient and recalcitrant if she disobeys her husband when he commands her to do an act of disobedience to Allaah. You have mentioned in the question that your husband asks you to pretend to be another woman during intercourse, and we have previously clarified in Fatwa 32898 that it is prohibited for the husband to imagine that he is having intercourse with a woman who is unlawful to him while he is having intercourse with his wife. Since this is a prohibited act, it is impermissible for you to help him commit it. Allaah The Exalted says (what means): {And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allaah; indeed, Allaah is severe in penalty.} [Quran 5:2]
The husband should seek treatment for himself. He should consult specialist physicians or psychiatrists. He is also advised to supplicate Allaah, recite the Quranic healing (Ruqyah), remember Allaah often and seek His forgiveness.
Allaah Knows best.