I.
We praise Allah, may He be Exalted, for guiding you to Islam, and we ask Him, may He be Glorified, to increase you in guidance and steadfastness, and to grant you a way out from what you are suffering of hardship and difficulties.
II.
If your family are forcing you to break your fast during the day in Ramadan, there is no sin on you for that, because you are excused. Allah, may He be Exalted, has lifted the burden of sin for one who makes an outward display of disbelief because of being forced to do so, on condition that his heart is steadfast in faith. He, may He be Exalted, says: {Those who disbelieve in Allah after having believed – except one who is compelled while his heart remains steadfast in faith – and willingly open their hearts to disbelief, upon them will be the wrath of Allah, and theirs will be a grievous punishment} [An-Nahl 16:106].
And the Prophet (blessings and peace of Allah be upon him) said: “My ummah is pardoned for errors and forgetfulness and what they are forced to do.” Classed as authentic (sahih) by al-Albani in Sahih Ibn Majah.
III.
If someone breaks his fast during Ramadan under compulsion, his fast is valid, but he should continue his fast and he does not have to make it up. This is the view of the Shafa`is, Hanbalis and Zahiris (literalists).
An-Nawawi (may Allah have mercy on him) said in Al-Majmu`, 6/353:
If the fasting person is forced to eat or drink, and he eats or drinks something, or a fasting woman is forced into intimacy and gives in, there are two well-known scholarly views as to whether the fast is invalidated, and hardly any scholar favoured one of the views over the other.
The view that is more likely to be correct is that the fast is not invalidated. Those who regarded this view as correct include the author in At-Tanbih, al-Ghazali in Al-Wajiz, al-`Abdari in Al-Kifayah, Ar-Rafa`i in Ash-Sharh, and others, and it is the correct view…
They quoted as evidence for the fast not being rendered invalid the fact that it was broken by force, because that was not done voluntarily. Therefore the individual is not sinning by eating, because in that case [according to Islamic teachings] he should eat, and he is not forbidden to eat. Thus he is like one who forgets [that he is fasting]; in fact it is more appropriate to say that his fast is not invalidated by that, because he is required [according to Islamic teachings] to eat in order to ward off harm from himself, unlike the one who forgets, because nothing is required of him in terms of whether he should or should not eat.
As for the evidence cited to support the other view, it is argued that he should eat in order to ward off harm from himself, so he is like the one who eats to ward off hunger and thirst. But the scholars differentiated between the two scenarios by noting that when a person is forced to eat, the action is involuntary, whereas hunger and thirst do not undermine his freedom to choose; rather they make his freedom to choose more evident. End quote.
Al-Bahuti said in Kashshaf al-Qina`, 2/320.
The one who is forced to eat does not break the fast, whether he is forced to do the action, meaning that he eats what he is forced to eat, or it is done to him, meaning that they pour water down his throat by force or when he is asleep, because of the general meaning of the Prophet’s words, “what they are forced to do.” End quote.
Al-Mirdawi said in Al-Insaf (7/424):
If he does what is mentioned above [of things that break the fast] deliberately, fully aware that he is fasting and by choice, his fast is rendered invalid. But if he does it by mistake because he forgot or was forced to do it – whether he is forced and pressured to break the fast until he does it, or it is done to him – the fast is not rendered invalid. This is the view of the madhhab, and a number of scholars narrated that from Imam Ahmad. End quote.
Ibn Hazm (may Allah have mercy on him) said:
As for the one who is forced to break the fast, his fast is complete and valid; there is nothing wrong with it and nothing is required of him ... this is the view of all our companions. End quote from Al-Muhalla, 4/361.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said:
Whoever is forced to do anything that breaks the fast and he does it, there is no sin on him and his fast is valid, because Allah, may He be Exalted, says: {And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful} [Al-Ahzab 33:5].
Moreover, Allah has ruled that one who is forced to commit an act of disbelief is not to be deemed a disbeliever; so it is more appropriate to apply the same principle in the case of one who is forced to do something less serious than that.
And the Prophet (blessings and peace of Allah be upon him) said: “My ummah is pardoned for errors and forgetfulness and what they are forced to do.” This is an authentic (hasan) hadith; many texts attest to its soundness. And he (blessings and peace of Allah be upon him) said: “Whoever is overcome by vomiting, then he is not required to make up (the fast), and whoever vomits on purpose, then he must make it up.” Narrated by the five except an-Nasa’i; classed as authentic by al-Hakim.
End quote from Majmu` Fatawa wa Rasa’il al-`Uthaymin, 19/194.
Based on that, and in the future, you should form the intention to fast the night before, and start the day fasting, in sha Allah. Then if your family forced you to break the fast, you can break the fast by consuming a small amount of food or drink, as much as will ward off their aggression from you, and will make them think that you are not fasting. Then you should complete your fast, and nothing further will be required of you.
Regarding the days on which you did not fast in the past, or the days on which you intended to fast from the night before and you started the day fasting, then you were forced to break the fast, your fast on those days is valid and you do not have to make it up.
As for the days on which you did not intend to fast from the night before, you must make them up, whenever you are able to do so.
The scholars are unanimously agreed that making up of missed fasts must be done before the next Ramadan begins.
They quoted as evidence for that the report narrated by al-Bukhari (1950) and Muslim (1146) from `A’ishah (may Allah be pleased with her), who said: I would owe Ramadan fasts, and I would not be able to make them up until Sha`ban, because of my duties towards the Messenger of Allah (blessings and peace of Allah be upon him).
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said:
What we learn from her keenness to do that in Sha`ban is that it is not permissible to delay making up missed fasts until the next Ramadan begins. End quote.
If someone cannot make up the missed fasts before the next Ramadan begins, there is nothing wrong with him delaying it until he is able to do it.
Shaykh Muhammad ibn `Uthaymin (may Allah have mercy on him) was asked:
A woman did not fast in Ramadan because of postpartum bleeding, and she was not able to make up the fasts, because of breastfeeding, before the next Ramadan began. What must she do?
He replied:
What is required of this woman is to make up the days when she did not fast, even if that is after the second Ramadan, because she only failed to make up the fasts between the first and second Ramadans because of a valid excuse. But if it is not difficult for her to make up the fasts during the winter, even if she does so intermittently, then she must do that, even if she is breastfeeding. She should be keen to do whatever she can to make up missed fasts from last Ramadan before the next Ramadan comes. But if she did not do that, there is no blame on her if she delayed it until the next Ramadan came.
End quote from Majmu` Fatawa ash-Shaykh Ibn `Uthaymin, 19, question no. 360.
Based on that, you should make up these days as best as you can, even if you do that intermittently, and offering expiation or feeding the poor cannot take the place of that.
We ask Allah, may He be Exalted, to accept your good deeds and to make things easy for you.
And Allah knows best.