An emperors daughter who collects her dead fathers body parts?
Yep, upon further research this sounds like Chaika the Coffin Princess. The anime came out a month ago in Japan, so it's relatively new (so I'm not completely sure, but Crunchyroll did for starters also start broadcasting it online at around the same time.)

The eponymous Chaika is the daughter of Arthur Gaz, who apparently was the former ruler of the Gaz Empire, according to the fan-made wiki. I haven't seen the anime or read the light novels, so I'm not sure, but judging from the list of names he has it seems reasonable to conclude that he was a bit of a tyrant.

Moreover, as might be suggested by the title, Chaika carries a coffin around most of the time. In the first episode, she runs into Toru Akura and his sister Akari, which is consistent with your description.

Here's the Anime News Network link.