Is it the fiancée's right to stipulate to her fiancé that they live in a separate dwelling, in an independent apartment, but above his mother's house, with her visiting and being kind to her, so that she may feel comfortable speaking with her future husband, especially since her fiancé will not be residing in the house anyway?

It is the wife's right to have an independent dwelling, and there is no religious blame upon her for requesting to move to another apartment other than the one where her husband's mother resides. Visiting the husband's mother and treating her kindly is a good deed that strengthens the marital relationship and earns the husband's رضا (satisfaction/contentment).