Was the revocable divorce (rajʿah) valid after my divorce from my wife, given that she remained in her family's home for six months or more before returning to me, and what is the ruling regarding our daughter after her death?

The default is that the رجعة (right to take back one's wife after an revocable divorce) does not occur if there is doubt about it after the waiting period (iddah) has expired. In this case, a new marriage contract is required. If the spouses were unaware of this, there is no sin upon them. As for the daughter, she is attributed to the husband because she resulted from intercourse believed to be permissible, for "the child is for the bed," and lineage is established even if the marriage was invalid.