Praise be to Allah.
If the mother was forced to have intercourse during Ramadan by her husband, then she does not have to offer expiation, because of the general meaning of the words of the Prophet (blessings and peace of Allah be upon him): “Allaah has forgiven for me my ummah their mistakes and forgetfulness, and what they are forced to do.” Narrated by Ibn Maajah (2043); classed as saheeh by al-Albaani in Saheeh Ibn Maajah. But if she went along with him willingly, then she has to make up that fast and offer expiation.
The scholars of the Standing Committee for Issuing Fatwas said concerning the ruling on one who has intercourse during the day in Ramadan:
What he has to do is free a slave. If he cannot do that, then he must fast for two consecutive months. If he cannot do that, then he must feed sixty poor persons, giving each one a mudd of wheat, and he has to make up a day to replace that day. As for the woman, if she did it willingly then the ruling is the same as that for a man, but if she was forced to do it then she does not have to do anything apart from making up that day. End quote. Fataawa al-Lajnah al-Daa’imah (10/302).
If the expiation is required of her, you have said that she is unable to fast; in that case it is sufficient for her to feed 60 poor persons.
See also the answer to question number 1672 for information on the expiation for intercourse during the day in Ramadan.
With regard to the father, he should have fasted two consecutive months and made up that day on which he broke the fast by having intercourse. As he has died and did not do that, then someone may volunteer to fast on his behalf, and fast two consecutive months, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever dies owing any (obligatory) fasts, his next-of-kin should make them up on his behalf.” Narrated by Muslim (1147).
It is not permissible to divide the two months between more than one person; rather it is stipulated that they should be fasted by one person so that it can truly be said that he fasted two consecutive months.
Or they may give food on his behalf to one poor person for each day.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
If the deceased was obliged to fast for two consecutive months, either one of his heirs may volunteer to fast them on his behalf, or they may feed one poor person for each day. End quote.
Al-Sharh al-Mumti’ (6/453).
And he said:
It is proven from the Prophet (blessings and peace of Allah be upon him) that if a person died owing an obligatory fast of Ramadan or a vow or expiation, then his next of kin may fast on his behalf –i.e., if he wishes. End quote.
Fataawa Noor ‘ala al-Darb, 20/199
Shaykh al-Sa’di (may Allah have mercy on him) said:
If a person dies owing days to be made up from Ramadan, and he recovered from the sickness (that prevented him from fasting) and did not fast them, then one poor person must be fed on his behalf every day, for a number of days equal to the number of days that he owed.
According to Shaykh Taqiy al-Deen [Ibn Taymiyah], if someone fasts it on his behalf, that is also acceptable. End quote. Irshaad Ooli’l-Basaa’ir wa’l-Albaab, p. 79
This food for the poor must be paid for from the estate. If someone donates it from his own wealth, there is nothing wrong with that.
And Allah knows best.