Are the questioner and his sister considered disobedient to their aunt if they refuse to repatriate the sister to their home country, and will the aunt's supplication harm them if they are in the right, and what is your advice for resolving this dispute?

If your paternal aunt has wronged you, then you are not being disobedient to her; rather, she is the one who severs ties and commits wrong. Her supplication against you without right will not harm you, for the Prophet, peace and blessings be upon him, said: "The supplication of a servant continues to be answered as long as he does not supplicate for a sin or the severing of kinship ties." It is advised not to forget her past kindness, and to treat her well, reward her, and maintain ties with her in a way that does not harm you, as mentioned in the Hadith from Abu Hurayrah: "If you are as you say, then it is as if you are feeding them hot ashes, and you will continue to have a supporter from Allah against them as long as you persist in that." Try to involve righteous people to reconcile between you and her, and responding to evil with good brings affection and repels the evil of Satan, in accordance with the Almighty's saying: "Repel evil with that which is better, and then the one between whom and you there was enmity will become as though he was a devoted friend."