Praise be to Allah.
Accommodation is one of the rights of the wife that is obligatory upon the husband according to scholarly consensus, because Allah, may He be exalted, has decreed that the husband is obliged to provide accommodation for the woman who is revocably divorced, as He says (interpretation of the meaning):
“Lodge them (the divorced women) where you dwell, according to your means”
So it is more appropriate that he be required to provide accommodation to the one who is still married. Moreover, Allah has enjoined kind and honourable treatment between spouses as He says (interpretation of the meaning):
“And live with them honourably”
Part of living with them honourably, as enjoined, is providing the wife with accommodation in which she and her wealth are secure. The wife cannot do without accommodation so as to shield her from prying eyes, and so that she can have her privacy and keep her wealth. Hence accommodation is one of the rights that she has over her husband.
The majority of Hanafi, Shafi‘i and Hanbali fuqaha are of the view that the wife has the right to accommodation separate from her husband’s relatives, and that she has the right to refuse to live with his father and mother or one of them.
See: al-Mawsoo‘ah al-Fiqhiyyah, 25/109
Please see also the answer to question no. 7653
If the wife agrees to live with the husband’s family, there is nothing wrong with that, because it is a yielding of her rights on her part. But that is subject to the conditions that she is safe from falling into haram situations with regard to being alone with a non-mahram or looking, and she has the right to change her mind about this agreement at any time, because her right to separate accommodation is not waived as a result of her giving it up.
What you mention about the possibility of being alone with one who is not permissible for you, and the possibility of him catching you unaware when you are not wearing hijab, confirms the necessity of hastening to find separate accommodation. It is not obligatory to obey his mother in this case, because obedience is only in that which is right and proper, and your staying in this family accommodation has two obvious negative outcomes:
1. It is impossible to relax and enjoy time together which both spouses want
2. There is a risk of falling into haram
So our advice to your husband is to hasten to find separate accommodation for you both, and to strive to please his mother with kind words, frequent visits, checking on how she is, gifts, and so on. And he should understand that his leaving his mother’s house is not regarded as disobedience towards her.
And Allah knows best.