Is the questioner sinful for refusing to help her aunt perform the Hajj pilgrimage, knowing that she wishes to perform Hajj with her own money, and has no one to support her?

Hajj is obligatory for those who are financially able. Whoever does not possess sufficient funds is not obligated to perform Hajj, nor is there any sin upon them. A person does not become financially able to perform Hajj merely because someone else donates the expenses for Hajj to them, nor are they obliged to accept this money. However, if the gift is accepted, then the Hajj performed with it is valid, the obligation is fulfilled by the pilgrim, and it is considered a legally accepted Hajj.