I would go to the interview, is your Aunt being buried? If she is, you could go to the graveside later and leave a lovely bouquet of flowers and a personal letter.
If there has been animosity then there could be trouble at the funeral. Which I am sure your Aunt wouldn't want.
My DH was in the situation where he was offered a massive promotion, going from agency (so not confirmed position) to an offer of a full-time position, his GF had just passed and whilst they were accommodating for him taking time off for a funeral, he knew that they needed the position filling immediately. Meaning that they would have to pass the promotion onto someone else. DH called his GM and she said his GF would want him to go for the job, that the funeral wasn't important. DH kept in touch with his GM daily and wrote a beautiful letter about his relationship with his GF and sent it with a bouquet of flowers and a big basket of fruit to his GM. She phoned and thanked him saying it was very comforting.
Unfortunately, it has been thrown in his face ever since, as he went NC with his DM/DF and they suddenly forgot all about the letter, the bouquet, the multiple phone calls and accused him of not caring at all. DH found it really distressing but when I asked him how he thought his GF would have felt about it, he said that his GF had told him that 'funerals are for the living, not the dead' and that he would have been more encouraging about his promotion.
He sometimes wonders if he should have gone to the funeral, but as things went because of his job we were able to buy our house. It was over a year before another position became available and that was given to the son of a higher up official. Which he would not have been offered. This sounds incredibly important, you have worked hard for this opportunity.
What matters is the love and relationship that you had with your Aunt. If you are on good terms with your cousins then I would maybe write a nice letter to them reminiscing about your Aunt. If not, then have your own little service to say goodbye, go to the graveside or light a candle and think about your Aunt. Is your Father going?