So sorry to hear that you are going through this.
At the end of the day, if your father has not left a will, has no parents, and no spouse, then anything he has will be split between you and any other children.
It sounds like is aunt wants whatever there is.
I don't really know what to advise about how to procede but I would suggest you get some basic legal advise.
I would assume you are entitled to sort his estate, and don't feel even a small amount of guilt for inheriting anything that IS LEGALLY YOURS.
It's NOT your aunts, (or anyone else, except your siblings) and if your father wanted to leave it to her then he needed to have made a will while he was alive.... Perhaps the fact he hasn't is "evidence" that he wanted it to go to you?
If he hasnt made a will, then the consequences are, that his children will inherit when he dies.
Dont feel any guilt about this...... This is what the law of the land dictates happens and that's absolutely nothing to do with you!!! It's just how it is.
Your aunt is very cheeky to even suggest you should gift it to her! How rude and presumptious of her to even think you might...