Is it permissible for a married woman to host her aunt, who lives 600 km away, if the aunt had taken care of her after her mother's death, and this visit is for the purpose of buying necessities for the aunt's son who is about to get married, while the husband objects to it?

It is not permissible for a woman to allow anyone into her husband's house except with his permission, based on the Prophet's (peace and blessings be upon him) saying: "And she should not allow anyone into his house except with his permission," and based on the hadith: "And you have the right that they do not allow anyone you dislike onto your bedding."

Some scholars are of the view that the husband does not have the right to prevent the wife's relatives from visiting her unless he fears corruption. In your situation, your husband should not prevent your aunt from visiting you without a valid reason, and he should honor her because she raised you when you were young.

As for your aunt staying with you, it is not permissible except with your husband's permission. You must maintain ties with your aunt and be kind to her, because the Prophet (peace and blessings be upon him) said: "The maternal aunt is like the mother."