A divorcee staying in a dwelling completely separate from her ex-husband's
There is no harm
in building an apartment for your mother in your father's house if your father permits it. (Part No. 17; Page No. 61) Moreover, this apartment should be completely separated as you have mentioned in your question. This is because there is no legal prohibition against doing this. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.