All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
One of the conditions for performing Hajj on behalf of a living person is that the latter is suffering from a state of permanent physical incapability and gives permission to another to do so on their behalf.
An-Nawawi defines the person who is physically incapable and for whom it is permissible to deputize another to perform Hajj on their behalf as “One who is too powerless to perform Hajj by himself and for whom no recovery is expected because of his old age, disability, or chronic, irremediable disease.”
That being the case, if your maternal aunt is not physically incapable in the way that we have mentioned, it is impermissible for her to deputize another to perform Hajj on her behalf, be it obligatory or voluntary. However, the Hanbali scholars hold it permissible for one who is capable of performing Hajj by themselves to deputize another to perform Hajj on their behalf of if that Hajj is voluntary.
In the cases in which it is permissible to deputize someone, it is held valid regardless of whether the deputy is a relative and whether he is one of the heirs or not. That your maternal aunt has daughters who are wealthy and have children does not impede you from acting as her deputy (to perform Hajj on her behalf) provided that it is permissible to deputize someone in principle, as has previously been mentioned.
Allaah Knows best.