Praise be to Allah.
Your looking after your aunt’s affairs and taking care of her are righteous deeds which will bring you closer to Allaah and increase you in reward and make your balance weigh heavily, but that is subject to the condition that your deed be done with the aim of seeking reward for the sake of Allaah. There is nothing wrong with your taking a payment in return for looking after her.
It is not permissible for you to take more than that by coercion or trickery. Allaah says (interpretation of the meaning):
“O you who believe! Eat not up your property among yourselves unjustly except it be a trade amongst you, by mutual consent”
And the Prophet (peace and blessings of Allaah be upon him) said: “It is not permissible (to take) the property of a Muslim unless he gives it willingly.” Narrated by Ahmad (20172); classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (1459).
It is not permissible for you – or for her – to deliberately harm the heirs, whether that is by giving gifts or establishing waqfs when one is alive, or by leaving a will for after one has died giving to someone who is not an heir. The Prophet (peace and blessings of Allaah be upon him) said: “There should be no harming or reciprocating harm.” Narrated by Ahmad and Ibn Maajah (2341); classed as saheeh by al-Albaani in Saheeh Ibn Maajah.
Ibn Rajab al-Hanbali (may Allaah have mercy on him) said: If he deliberately seeks to harm his heirs by leaving one-third of the estate to a stranger in his will, then he is sinning because of that malicious intent. But should his will be cancelled if it is proven or not? Ibn ‘Atiyah narrated that Maalik said it should be cancelled. And it was said that this is an analogy to the view of Ahmad. End quote.
Jaami’ ‘Uloom al-Hakam (1/305).
Shaykh Siddeeq Hasan Khaan (may Allaah have mercy on him) said:
Whoever sets up a waqf for the purpose of harming his heirs, his waqf is invalid, because that is something for which Allaah has not given permission. Allaah has only given permission for ongoing charity that benefits the one who gives it, not for that which is an ongoing sin and brings an ongoing punishment. Allaah has forbidden harming others in His Book in general terms and in specific terms. The Prophet (peace and blessings of Allaah be upon him) also forbade it in general terms, as in the hadeeth: “There is no harming or reciprocating harm in Islam.” End quote.
Al-Rawdat al-Nadiyyah, 2/154.
In your question you say that among the things your siblings rebuked you for is your “taking advantage of the fact that your aunt is not qualified.” If what they said is true and your aunt is not qualified to dispose of wealth, such as if she is not of sound mind or she is foolish and wastes money, then what she has done by giving you her wealth is invalid according to sharee’ah and it is not permissible for you to take possession of it, because she is not qualified to dispose of her wealth.
Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said:
All words and contracts are subject to the condition that a person have the ability of discernment and reasoning. If a person has no power of discernment and reason, then his words do not carry any weight at all according to sharee’ah, as the Prophet (peace and blessings of Allaah be upon him) said: “In the body there is a piece of flesh which, if it is sound, the entire body will be sound, and if it is corrupt, the entire body will be corrupt. It is the heart.” If the reasoning of the heart is missing, with which a person speaks and engages in dealings, how can it be permissible to allow him to command and deny, or affirm possession or remove it? This is based on common sense as well as the statements of sharee’ah.
Contracts and other dealings are subject to the condition of intentions, as the Prophet (peace and blessings of Allaah be upon him) said: “Deeds are but by intentions.” I have explained this principle in the book Bayaan al-Daleel ‘ala Batlaan al-Tahleel, where I stated that any word that is uttered unintentionally by the speaker due to forgetfulness, a slip of the tongue or lack of reasoning does not result in a ruling. End quote.
Majmoo’ al-Fataawa 33/107.
If your aunt is of sound mind, then her disposing of her wealth by giving it as a gift, giving it in charity or any other way is valid.
Shaykh ‘Abd-Allaah ibn Jibreen (may Allaah preserve him) said, in a ruling on a similar issue:
It is permissible for the husband, when he is healthy and still alive, to give his wife whatever he wants in return for her patience, good service or money came into his possession but belonged to her, such as left-over dowry etc, so long as he does not do that in order to harm the other heirs, and that is not limited to one-quarter of the wealth or any other amount.
Similarly, with regard to the wife, she may give her husband whatever she wants of her wealth or dowry, because Allaah says (Interpretation of the meaning):
“but if they, of their own good pleasure, remit any part of it to you, take it, and enjoy it without fear of any harm (as Allaah has made it lawful)”
But that is not permissible in the event of sickness, because then it is regarded as making a will in favour of an heir. End quote.
Fataawa Islamiyyah (3/29)
Your siblings should note that your aunt is not obliged to give gifts equally to all her brother’s children. Fairness in gift-giving is enjoined only when giving to one's own children, but in the case of others it is not required that one give equally.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) said:
It is permissible for a person to show preference to some of his heirs over others if this is done when he is in good health, except in the case of his own children, where it is not permissible to show preference to some of them over others. End quote.
Fataawa Islamiyyah (3/30).
To sum up:
If your aunt is of sound mind and she gave you this wealth by her own choice and willingly, without any pressure or trickery on your part, and without her intending any harm to her heirs, then this giving is valid and is not against sharee’ah.
But if she is not of sound mind or she gave it unwillingly, or she intended to harm the other heirs, then this gift is haraam and it is not valid, and her wealth is still hers.
In this case, you may take a payment from her in return for your serving her and administering her wealth, so long as this payment is commensurate with the work done and there is no exaggeration therein.
And Allaah knows best.