Is it permissible for a woman to emigrate in the path of Allah without a mahram if she lives with family members who tempt her away from her religion and compel her to do things that contradict Islamic law, and are there any religious texts that support this?

The daughter must try to rid herself of and distance herself from the father who insults religion, enjoins evil, and forbids good. This must be done in a lawful manner, so that she does not emigrate to an unsafe place or travel alone. Emigration is only permissible to a country where a Muslim can practice their religion, and a woman's travel without a mahram is not permissible except out of necessity. The girl can search for a righteous husband who can deliver her from this situation, or seek assistance from righteous people of good.