Firstly: 

The scholars differed as to those to whom zakaat al-fitr should be given. The majority of them are of the view that it may given to any of the eight categories to whom the zakaah of wealth should be given. Some of them were of the view that it should be given to all of these eight categories, and others were of the view that it should b egiven only to the poor and needy. 

It says in al-Mawsoo’ah al-Fiqhiyyah (23/344): 

The fuqaha’ differed concerning who should be given zakaat al-fitr and there are three views: the majority are of the view that it is permissible to divide it among the eight categories to whom the zakaah of wealth may be given; the Maalikis – and it was also narrated from Ahmad and was the view favoured by Ibn Taymiyah – are of the view that it should be given only to the poor and needy; and the Shaafa’is are of the view that it should be divided among the eight categories or whoever of them are available. End quote. 

Shaykh al-Islam Ibn Taymiyah refuted the first and third views in Majmoo’ al-Fataawa (25/73-78). He explained that zakaat al-fitr has to do with the number of people, not wealth. Among the things he said there was the following: 

Hence Allaah has enjoined that it be in the form of food, just as He has enjoined that expiation be in the form of food. Based on this view, it is not permissible to give zakaat al-fitr except to those who are entitled to receive food given as expiation, and they are those who take it because they are in need of it, so it should not be given to those whose hearts are to be reconciled or to slaves etc. This is the strongest view, based on the evidence. 

The weakest opinion is that of those who say that it is obligatory for every Muslim to give his sadaqat al-fitr to twelve or eighteen or twenty-four or thirty-two or twenty-eight and so on, because this is contrary to the practice of the Muslims at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him) and the Rightly-Guided Caliphs and all the Sahaabah. No Muslim did this at that time, rather the Muslim would give his own sadaqat al-fitr and the sadaqat al-fitr of his family to one Muslim. If they had seen someone sharing the saa’ between umpteen people, giving each one a handful they would have denounced that in the strongest terms and regarded it as a reprehensible innovation and objectionable deed. The Prophet (peace and blessings of Allaah be upon him) stated that the enjoined amount is a saa’ of dates, or a saa’ of barley, or half a saa’ or a saa’ of wheat, based on the amount that is sufficient for one poor person, and he stipulated that it should be food for them on the day of Eid to make them independent of means. If the poor person takes a handful of food he will not benefit from it and it will not go very far. The same applies to the debtor and wayfarer – if they take a handful of wheat it will not benefit them. … Islam is above such a reprehensible action which no wise person would approve of and which none of the salaf or imams of this ummah did. 

Moreover, the words of the Prophet (peace and blessings of Allaah be upon him), “as food for the poor”, show that this is the right of the poor person, as Allaah says in the verse of zihaar (interpretation of the meaning): “should feed sixty Masaakeen (poor)” [al-Mujaadilah 58:4]. So if it is not permissible to give it to these eight categories, then the same applies here. End quote. 

Based on this, the most correct of these three opinions is the second one, which is that sadaqat al-fitr should be given to the poor and needy, and no one else. This is what was regarded as most correct by Shaykh al-‘Uthaymeen (may Allaah have mercy on him), as it says in al-Sharh al-Mumti’ (6/117). 

Secondly: 

If zakaat of one’s wealth and zakaat al-fitr are given to relatives who are entitled to it, that is better than giving it to others who are entitled to it, because in this case it is both zakaah and upholding ties of kinship. But that is subject to the condition that this relative is not one of those on whom the one who is giving the zakaah is obliged to spend.  

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) was asked about the ruling on giving zakaat al-fitr to poor relatives. 

He replied: 

It is permissible to give zakaat al-fitr and the zakaah of one's wealth to poor relatives, and indeed giving it to relatives is better than giving it to strangers, because giving it to relatives is both charity and upholding the ties of kinship. But that is subject to the condition that by giving it he is not protecting his wealth, which would be the case if the poor person is one on whom he is obliged to spend. In that case it is not permissible for him to meet the other person’s needs with any of his zakaah, because if he does that then he is saving his wealth with what he gives of zakaah, and that is not permissible or allowed. But if he is not obliged to spend on him, then he may give his zakaah to him, and in fact giving his zakaah to him is better than giving it to a stranger, because the Prophet (peace and blessings of Allaah be upon him) said: “Your charity given to a relative is both charity and upholding the ties of kinship.” End quote. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen (18/question no. 301). 

Conclusion: 

If your aunt is poor then she is entitled to zakaah, even if she owns half a dunam, but it is better for her to sell it and thus make herself independent of means so that she will not be dependent on people’s gifts. 

The Muslims should not leave their relatives until the month of Ramadaan is nearly over and then check on them and give them a saa’ of food, rather the Muslims should always check on the poor and needy and hasten to give them what they need of food, money and clothing, and this is required more so of the rich who should check on their poor relatives. 

And Allaah knows best.