Is it permissible for the wife to refuse her husband due to his not living in the marital home, if the husband only asks her to go to the house for the purpose of intimacy, bearing in mind that they live with his mother and the wife is harmed by this, especially since she has a child?

A wife has the right to an independent dwelling, unless she waives that right. If the husband refuses to provide it, the wife has the right to refuse intimacy until she obtains her right, because the husband's right to intimacy is conditioned upon his fulfilling his wife's rights, including maintenance and housing.