Is it permissible for a father to sell his children a house from his possessions before his marriage, while his children also own another house in partnership with his new wife and her daughter?

First: What you did by requesting the registration of the first house in your name was not your right, due to your father's unwillingness, and because he was not permitted to give up his property in exchange for his marriage.

Second: If you are certain that your father's registration of the house in your name was done under duress, then you must include it in the estate to be inherited with the rest of the heirs, based on the Almighty's saying: (O you who have believed, do not consume one another's property unlawfully but only [in lawful] trade by mutual consent.) and according to the Prophet's (peace be upon him) saying: (Indeed, nothing of a man's brother's wealth is lawful for him except with his cheerful consent.)

Third: However, if your father gave you the house willingly, or became willing afterwards and before conceiving children with his second wife, then it is lawful for you and does not need to be included in the inheritance.