I.
It appears from your question that your mother is not sick at present, but she has to reduce her food intake so that she will not vomit. The fact that she eats little could lead to harm, or possibly make her weak, or cause some other obvious hardship. Based on that:
- If the doctor who knows her situation said that fasting could harm her when she can only eat a little, then she may break the fast and make it up, even if she does not fast for the entire month.
- If it is merely the matter of weakness, such as if she becomes exhausted and wants to sleep, this does not make it permissible not to fast.
In principle, she is required to fast, so she must form the intention to fast from the night before, and limit her sahur meal to a small amount that will not harm her. Then if, whilst fasting, she experiences exhaustion or weakness that does not harm her, she must fast, and it is prohibited for her to break the fast.
If she can’t help vomiting and does not do that deliberately, then her fast is valid, because of the report narrated by at-Tirmidhi (720) from Abu Hurayrah (may Allah be pleased with him), that the Prophet (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.” Al-Albani classed it as sahih in Sahih at-Tirmidhi.
Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni (2/23): The one who vomits on purpose must make it up, and the one who is overcome by vomiting does not have to do anything.
What is meant by vomiting on purpose is that he makes himself vomit deliberately. What is meant by being overcome by vomiting is that it happens involuntarily and the person cannot help it.
So the one who vomits on purpose must make it up, because his fast is rendered invalid by that, but the one who is overcome by vomiting does not have to do anything.
This is the view of most of the scholars. Al-Khattabi said: I do not know of any difference of opinion concerning that among the scholars. End quote.
- If that results in obvious hardship whilst fasting, then she may eat just enough to maintain her strength, then refrain from eating for the rest of the day and make that day up later on.
She should do this every day, like people who have physically demanding jobs, such as blacksmiths, bakers and the like.
In Al-Mawsu`at al-Fiqhiyyah (28/57) it says: The Hanafis say: For one whose work is physically demanding and he needs to earn a living, such as bakers and harvesters, if he knows that if he does his work he will be harmed to the extent that allows him to break the fast, it is prohibited for him to break the fast before he encounters that level of hardship. End quote.
It says in Fatawa al-Lajnat al-Da’imah (10/233): In the case of one for whom fasting is obligatory, it is not permissible for him to break the fast during the day in Ramadan just because he is working, but if he faces great hardship that leaves him no choice but to break the fast during the day, then he may break the fast and eat as much as will ward off hardship, then he must refrain from eating until sunset, then break fast with the people, and he must make up that day on which he broke the fast. End quote.
Thus you will realise that so long as the doctor did not say that fasting will harm her, she is Islamically obliged to fast, then she should see whether she experiences weakness or obvious hardship, in which case she should do what we mentioned in detail above.
II.
If your mother does not fast, following doctor's orders, or because she experiences obvious hardship, then she is obliged only to make up the fasts.
As for feeding the poor, that is required of one who is sick and has no hope of recovery, and old men and old women who cannot fast.
You should understand that it is possible to compensate for reduced intake of food by taking nutritional supplements, after consulting the doctor.
Whatever the case, you must be careful to avoid breaking the fast with no excuse, because this is a major sin.
Adh-Dhahabi (may Allah have mercy on him) said in Al-Kaba’ir, p. 64: It is well established among the believers that whoever does not fast Ramadan without being sick and with no excuse (that would make that permissible) is worse than the one who commits zina and the one who is addicted to alcohol; in fact they dobt that he is even a Muslim, and they accuse him of being a heretic and evildoer. End quote.
One of the soundly narrated texts which issue a warning against not fasting is that which was narrated by Ibn Khuzaymah (1986) and Ibn Hibban (7491) from Abu Umamah al-Bahili, who said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “Whilst I was sleeping, [I saw in my dream] two men who came and took me by my arms and brought me to a rugged mountain. They said: Climb up. I said: I am not able to do that. They said: We will help you. So I climbed up until I reached the top of the mountain, and there I heard loud screams. I said: What are these screams? They said: This is the howling of the people of Hell. Then they took me further, and I saw some people who were suspended upside down by their Achilles’ tendons, and the sides of their mouths were torn and were pouring with blood. I said: Who are these people? He said: These are the people who broke the fast before the right time to break the fast came.” Al-Albani classed it as sahih in Sahih Mawarid az-Zam`an, no. 1509.
Al-Albani (may Allah have mercy on him) said: This is the punishment of those who fasted then broke the fast deliberately before the time of iftar came, so how about those who do not fast in the first place? We ask Allah to keep us safe and sound in this world and the hereafter. End quote.
And Allah knows best.