Is it permissible to be married at the same time to my wife and her father's wife (knowing that my wife is not her daughter)?

It is permissible for a man to marry the stepmother of his wife, as long as she is not his wife's mother. There is no objection to this, even if she is the daughter of her husband (the stepmother's husband) with her, because there is no prohibited familial relationship between them. Those who are prohibited from being married simultaneously are two sisters, a woman and her maternal aunt, and a woman and her paternal aunt. Allah has made permissible what is beyond that, by His saying: "And lawful for you are [all others] beyond these, [provided] that you seek them with your wealth."

As for the mother and her daughter: - If the daughter is the wife, her mother is permanently forbidden to the husband as soon as the marriage contract is concluded. - If the mother is the wife: - If the husband has consummated the marriage with her (had intercourse with her), the daughter is permanently forbidden to him. - If he has not consummated the marriage with her, the daughter is forbidden to him until he separates from her mother, based on the Almighty's saying: "And your wives' mothers, and your stepdaughters under your guardianship, [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you."