I don't think her dad picked her up. When the media first approached him a week or more after the alleged event, he knew nothing about it and said he'd seen his daughter that (next) day and she was fine, and had dropped her car off there and left. He didn't know his daughter was the woman the story was centered around, didn't know she'd been in the hospital, nothing. So somebody else picked her up, probably her BF, and then they brought her car to her father's house where she left her kids and her car. That was his first story, and since he seemed to be caught off guard, it appears to be the only truthful story he's told.
I'll have to go back to look at the news reports, but his story as I recall was that he DID know she was in the hospital (in fact I think one of the stories had him going to the hospital in the early morning hours and then going back home, perhaps without even seeing her), but that he DID NOT know she was supposedly a rape victim until later. I agree that the impression I got from the reports is that the BF probably drove her home from the hospital, and may have been there the whole 5 hrs.