Is a woman considered to have been legitimately returned to her husband simply by the act of kissing or intercourse — by force — after a first divorce, while she is still in her father's house and does not wish to return to him?

This woman is a stranger to the questioner, and it is not permissible for him to establish a relationship with her. He must repent to Allah.

As for the husband's action with his wife, the preponderant opinion is that a raj'ah (revocation of divorce) does not occur through action alone, but only with intention. If the husband did not intend to take his wife back, then she is still in her iddah (waiting period), and he has the right to take her back as long as her iddah has not expired. During the iddah, she has the marital rights of maintenance, clothing, and housing. If the iddah expires and he has not taken her back, then she is free to marry whomever she wishes.

It is not permissible to propose to this woman or allude to a proposal until her iddah has expired, because she is still married to another. The iddah of a divorced woman is what the Shariah has specified, and the husband's designation of three months is of no account.