Whatever she has said about Henry’s father ,whether it was true or not ,and whatever has actually happened between them in the past ,i think it’s pretty clear from her behavior that her feelings towards him are negative.
Yes her feelings are negative, but I think it’s important to keep in mind the difference between hurt and hate. In that epp I got the distinct impression that it was still really hurt about what happened, and that that hurt hadn’t ever really healed. The fact that that still hasn’t healed makes me think that she still has feelings for him.
As for her not having anything of his father’s, I think she lied. I think it was a painful subject that she was trying to avoid as much as possible and i don’t think it would have been possible to explain the car without going into how she got it. Even if she wasn’t trying to avoid talking about Henry’s father, she probably didn’t want to explain how she got it (see promo 2).