What is the ruling on not praying with a father who rushes his prayer and does not perform it with tranquility, and is it permissible to repeat the prayer after performing it with him?

If the father performs the obligatory minimum of tranquility (ṭumaʾnīnah) but omits the recommended (mustaḥabb) amount, then your prayer behind him is valid, and you do not need to repeat it. However, if he does not perform the obligatory minimum of tranquility, then his prayer is invalid, and so is the prayer of those behind him, and they must repeat it. In this case, the female congregant (maʾmūmah) can pray individually. To avoid animosity, the female congregant can pray behind him with the intention of a parallel prayer (ṣalāt al-muḥādhāh), whereby she outwardly follows him in actions without intending to be led by him (iqtidāʾ), and thus her prayer would be valid.